Qiao, Yu; Xiong, Xiangtuan Simultaneous determination of the space-dependent source and initial value for a two-dimensional heat conduction equation. (English) Zbl 07741347 Comput. Math. Appl. 147, 25-37 (2023). MSC: 35R30 65M32 35R25 35K05 65M30 PDFBibTeX XMLCite \textit{Y. Qiao} and \textit{X. Xiong}, Comput. Math. Appl. 147, 25--37 (2023; Zbl 07741347) Full Text: DOI
Yang, Shuping; Xiong, Xiangtuan; Pan, Ping; Sun, Yue Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation. (English) Zbl 1487.65144 Numer. Algorithms 90, No. 2, 881-903 (2022). MSC: 65M32 65M30 65J20 65M12 65M15 35B45 35B65 35K05 35R30 35R25 26A33 35R11 35Q79 PDFBibTeX XMLCite \textit{S. Yang} et al., Numer. Algorithms 90, No. 2, 881--903 (2022; Zbl 1487.65144) Full Text: DOI
Xue, Xuemin; Xiong, Xiangtuan; Zhang, Yuanxiang Two fractional regularization methods for identifying the radiogenic source of the helium production-diffusion equation. (English) Zbl 1525.65090 AIMS Math. 6, No. 10, 11425-11448 (2021). MSC: 65M32 35K05 35R30 65J10 PDFBibTeX XMLCite \textit{X. Xue} et al., AIMS Math. 6, No. 10, 11425--11448 (2021; Zbl 1525.65090) Full Text: DOI
Ma, Rui; Xiong, Xiangtuan; Amin, Mohammed Elmustafa The method of fundamental solution for a radially symmetric heat conduction problem with variable coefficient. (English) Zbl 1499.65225 J. Partial Differ. Equations 34, No. 3, 258-267 (2021). MSC: 65K05 35R30 65M32 PDFBibTeX XMLCite \textit{R. Ma} et al., J. Partial Differ. Equations 34, No. 3, 258--267 (2021; Zbl 1499.65225) Full Text: DOI
Xiong, Xiangtuan; Shi, Wanxia; Xue, Xuemin Determination of three parameters in a time-space fractional diffusion equation. (English) Zbl 1484.35395 AIMS Math. 6, No. 6, 5909-5923 (2021). MSC: 35R11 49N45 65M32 PDFBibTeX XMLCite \textit{X. Xiong} et al., AIMS Math. 6, No. 6, 5909--5923 (2021; Zbl 1484.35395) Full Text: DOI
Yang, Shuping; Xue, Xuemin; Xiong, Xiangtuan A modified quasi-boundary value method for a backward problem for the inhomogeneous time conformable fractional heat equation in a cylinder. (English) Zbl 07479286 Inverse Probl. Sci. Eng. 29, No. 9, 1323-1342 (2021). MSC: 35R25 35R30 65J20 65M30 PDFBibTeX XMLCite \textit{S. Yang} et al., Inverse Probl. Sci. Eng. 29, No. 9, 1323--1342 (2021; Zbl 07479286) Full Text: DOI
Xiong, Xiangtuan; Xue, Xuemin; Li, Zhenping On a weighted time-fractional asymptotical regularization method. (English) Zbl 1524.65215 J. Comput. Appl. Math. 394, Article ID 113579, 13 p. (2021). MSC: 65J20 65J10 47A52 35R30 65M32 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Comput. Appl. Math. 394, Article ID 113579, 13 p. (2021; Zbl 1524.65215) Full Text: DOI
Shi, Wanxia; Xiong, Xiangtuan; Xue, Xuemin A fractional-order quasi-reversibility method to a backward problem for the time fractional diffusion equation. (English) Zbl 1475.65111 J. Comput. Appl. Math. 394, Article ID 113552, 14 p. (2021). MSC: 65M32 65M12 65M15 35B65 35B20 26A33 35R11 35R30 PDFBibTeX XMLCite \textit{W. Shi} et al., J. Comput. Appl. Math. 394, Article ID 113552, 14 p. (2021; Zbl 1475.65111) Full Text: DOI
Yang, Shuping; Xiong, Xiangtuan; Nie, Yan Iterated fractional Tikhonov regularization method for solving the spherically symmetric backward time-fractional diffusion equation. (English) Zbl 1467.65090 Appl. Numer. Math. 160, 217-241 (2021). Reviewer: Michael Jung (Dresden) MSC: 65M22 65M15 65J20 60H40 35R11 35R30 35R25 PDFBibTeX XMLCite \textit{S. Yang} et al., Appl. Numer. Math. 160, 217--241 (2021; Zbl 1467.65090) Full Text: DOI
Yang, Shuping; Xiong, Xiangtuan; Han, Yaozong A modified fractional Landweber method for a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. (English) Zbl 07476512 Int. J. Comput. Math. 97, No. 11, 2375-2393 (2020). MSC: 65-XX 35R25 35R30 65J20 65M30 PDFBibTeX XMLCite \textit{S. Yang} et al., Int. J. Comput. Math. 97, No. 11, 2375--2393 (2020; Zbl 07476512) Full Text: DOI
Xiong, Xiangtuan; Bai, Enpeng An optimal filtering method for the sideways fractional heat equation. (Chinese. English summary) Zbl 1463.65351 J. Northwest Norm. Univ., Nat. Sci. 56, No. 3, 14-16, 47 (2020). MSC: 65N20 65N15 65T50 35R11 35K05 35B65 PDFBibTeX XMLCite \textit{X. Xiong} and \textit{E. Bai}, J. Northwest Norm. Univ., Nat. Sci. 56, No. 3, 14--16, 47 (2020; Zbl 1463.65351) Full Text: DOI
Zheng, Zhenming; Li, Zhenping; Xiong, Xiangtuan An improved error bound on the boundary inversion for a sideways heat equation. (English) Zbl 1437.65127 São Paulo J. Math. Sci. 14, No. 1, 287-300 (2020). MSC: 65M32 65M30 65M06 65M15 65K10 65J20 35R30 35R25 35K05 35B45 35B65 PDFBibTeX XMLCite \textit{Z. Zheng} et al., São Paulo J. Math. Sci. 14, No. 1, 287--300 (2020; Zbl 1437.65127) Full Text: DOI
Yang, Shuping; Xiong, Xiangtuan A Tikhonov regularization method for solving an inverse heat source problem. (English) Zbl 1431.65251 Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 441-452 (2020). MSC: 65R32 35R30 PDFBibTeX XMLCite \textit{S. Yang} and \textit{X. Xiong}, Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 441--452 (2020; Zbl 1431.65251) Full Text: DOI
Xiong, Xiangtuan; Xue, Xuemin Fractional Tikhonov method for an inverse time-fractional diffusion problem in 2-dimensional space. (English) Zbl 1431.65160 Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 25-38 (2020). MSC: 65M32 65M30 35R11 35R30 PDFBibTeX XMLCite \textit{X. Xiong} and \textit{X. Xue}, Bull. Malays. Math. Sci. Soc. (2) 43, No. 1, 25--38 (2020; Zbl 1431.65160) Full Text: DOI
Yang, Shuping; Xiong, Xiangtuan A fractional Tikhonov regularisation method for finding source terms in a time-fractional radial heat equation. (English) Zbl 1462.35455 East Asian J. Appl. Math. 9, No. 2, 386-408 (2019). MSC: 35R25 35R30 35R11 35K20 65J20 65M30 PDFBibTeX XMLCite \textit{S. Yang} and \textit{X. Xiong}, East Asian J. Appl. Math. 9, No. 2, 386--408 (2019; Zbl 1462.35455) Full Text: DOI
Han, Yaozong; Xiong, Xiangtuan; Xue, Xuemin A fractional Landweber method for solving backward time-fractional diffusion problem. (English) Zbl 1442.65224 Comput. Math. Appl. 78, No. 1, 81-91 (2019). MSC: 65M30 65M12 35R11 PDFBibTeX XMLCite \textit{Y. Han} et al., Comput. Math. Appl. 78, No. 1, 81--91 (2019; Zbl 1442.65224) Full Text: DOI
Chen, Yawen; Xiong, Xiangtuan Fractional Tikhonov method of a non-characteristic Cauchy problem for a parabolic equation. (Chinese. English summary) Zbl 1449.65227 J. Shandong Univ., Nat. Sci. 54, No. 12, 120-126 (2019). MSC: 65M30 65M15 35R11 26A33 65J20 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{X. Xiong}, J. Shandong Univ., Nat. Sci. 54, No. 12, 120--126 (2019; Zbl 1449.65227) Full Text: DOI
Xiong, Xiangtuan; Xue, Xuemin A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation. (English) Zbl 1428.35674 Appl. Math. Comput. 349, 292-303 (2019). MSC: 35R11 35R30 PDFBibTeX XMLCite \textit{X. Xiong} and \textit{X. Xue}, Appl. Math. Comput. 349, 292--303 (2019; Zbl 1428.35674) Full Text: DOI
Ren, Liting; Xiong, Xiangtuan The Fourier method for the Cauchy problem of the Helmholtz equation with inhomogeneous Dirichlet data. (Chinese. English summary) Zbl 1463.65271 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 43, No. 2, 184-187 (2019). MSC: 65M30 65T50 35R25 35J05 35B65 65M12 65M15 PDFBibTeX XMLCite \textit{L. Ren} and \textit{X. Xiong}, J. Jiangxi Norm. Univ., Nat. Sci. Ed. 43, No. 2, 184--187 (2019; Zbl 1463.65271) Full Text: DOI
Amin, Mohammed Elmustafa; Xiong, Xiangtuan Source identification problems for radially symmetric and axis-symmetric heat conduction equations. (English) Zbl 1432.65137 Appl. Numer. Math. 138, 1-18 (2019). MSC: 65M32 35K20 35R30 80A23 PDFBibTeX XMLCite \textit{M. E. Amin} and \textit{X. Xiong}, Appl. Numer. Math. 138, 1--18 (2019; Zbl 1432.65137) Full Text: DOI
Xiong, Xiangtuan; Zhuang, E.; Xue, Xuemin; Qian, Zhi A regularization framework for mildly ill-posed problems connected with pseudo-differential operator. (English) Zbl 1440.65281 J. Comput. Appl. Math. 341, 1-11 (2018). Reviewer: Dinh Nho Hào (Hanoi) MSC: 65R30 65D25 35R30 53C35 65M32 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Comput. Appl. Math. 341, 1--11 (2018; Zbl 1440.65281) Full Text: DOI
Zhuang, E.; Xiong, Xiangtuan; Xue, Xuemin; Ma, Xiaojun Regularization method for solving a backward heat conduction problem based on wavelet shrinkage. (Chinese. English summary) Zbl 1438.65217 Commun. Appl. Math. Comput. 32, No. 4, 831-840 (2018). MSC: 65M30 65M32 35B65 35K05 80A19 35Q79 35R30 65T60 PDFBibTeX XMLCite \textit{E. Zhuang} et al., Commun. Appl. Math. Comput. 32, No. 4, 831--840 (2018; Zbl 1438.65217) Full Text: DOI
Wang, Jianlin; Xiong, Xiangtuan; Cao, Xiaoxiao Fractional Tikhonov regularization method for a time-fractional backward heat equation with a fractional Laplacian. (English) Zbl 1438.65216 J. Partial Differ. Equations 31, No. 4, 333-342 (2018). MSC: 65M30 65M32 65M12 26A33 35R11 65J20 PDFBibTeX XMLCite \textit{J. Wang} et al., J. Partial Differ. Equations 31, No. 4, 333--342 (2018; Zbl 1438.65216) Full Text: DOI Link
Xiong, Xiangtuan; Ma, Xiaojun A backward identification problem for an axis-symmetric fractional diffusion equation. (English) Zbl 1488.65387 Math. Model. Anal. 22, No. 3, 311-320 (2017). MSC: 65M32 35R30 35R11 65M30 65M12 PDFBibTeX XMLCite \textit{X. Xiong} and \textit{X. Ma}, Math. Model. Anal. 22, No. 3, 311--320 (2017; Zbl 1488.65387) Full Text: DOI
Cheng, Qiang; Xiong, Xiangtuan An iterative method for an inverse source problem of a time-fractional diffusion equation. (Chinese. English summary) Zbl 1399.65224 Math. Numer. Sin. 39, No. 3, 295-308 (2017). MSC: 65M32 65M30 35R11 76R50 PDFBibTeX XMLCite \textit{Q. Cheng} and \textit{X. Xiong}, Math. Numer. Sin. 39, No. 3, 295--308 (2017; Zbl 1399.65224)
Xiong, Xiangtuan; Cao, Xiaoxiao; He, Shumei; Wen, Jin A modified regularization method for a Cauchy problem for heat equation on a two-layer sphere domain. (English) Zbl 1410.35054 Appl. Math. Comput. 290, 240-249 (2016). MSC: 35K15 35R25 PDFBibTeX XMLCite \textit{X. Xiong} et al., Appl. Math. Comput. 290, 240--249 (2016; Zbl 1410.35054) Full Text: DOI
Xiong, Xiangtuan; Zheng, Zhenming; Zhou, Qian Tikhonov method for the time fractional diffusion equation in 2-D space and error estimation. (Chinese. English summary) Zbl 1374.65156 J. Northwest Norm. Univ., Nat. Sci. 52, No. 2, 9-12 (2016). MSC: 65M30 65M15 35K15 35R25 35R11 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Northwest Norm. Univ., Nat. Sci. 52, No. 2, 9--12 (2016; Zbl 1374.65156) Full Text: DOI
Li, Jinmei; Xiong, Xiangtuan Semi-discretization difference approximation for a Cauchy problem of heat equation in two-dimensional space. (English) Zbl 1349.65410 J. Partial Differ. Equations 28, No. 4, 315-331 (2015). MSC: 65M32 65M06 65M15 65M30 35K05 35R30 65M20 PDFBibTeX XMLCite \textit{J. Li} and \textit{X. Xiong}, J. Partial Differ. Equations 28, No. 4, 315--331 (2015; Zbl 1349.65410) Full Text: DOI
Qian, Zhi; Hon, Benny Y. C.; Xiong, Xiang Tuan Numerical solution of two-dimensional radially symmetric inverse heat conduction problem. (English) Zbl 1515.35355 J. Inverse Ill-Posed Probl. 23, No. 2, 121-134 (2015). MSC: 35R30 35R25 65M32 65R32 PDFBibTeX XMLCite \textit{Z. Qian} et al., J. Inverse Ill-Posed Probl. 23, No. 2, 121--134 (2015; Zbl 1515.35355) Full Text: DOI
Xiong, Xiangtuan; Fan, Xiaoyan; Li, Ming Spectral method for ill-posed problems based on the balancing principle. (English) Zbl 1335.35289 Inverse Probl. Sci. Eng. 23, No. 2, 292-306 (2015). MSC: 35R25 PDFBibTeX XMLCite \textit{X. Xiong} et al., Inverse Probl. Sci. Eng. 23, No. 2, 292--306 (2015; Zbl 1335.35289) Full Text: DOI
Xiong, Xiangtuan; Zhao, Liping; Hon, Y. C. Stability estimate and the modified regularization method for a Cauchy problem of the fractional diffusion equation. (English) Zbl 1294.65090 J. Comput. Appl. Math. 272, 180-194 (2014). MSC: 65M12 65M15 65M30 35R11 35K05 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Comput. Appl. Math. 272, 180--194 (2014; Zbl 1294.65090) Full Text: DOI
Li, Ming; Xi, Xiang-Xiang; Xiong, Xiang-Tuan Regularization for a fractional sideways heat equation. (English) Zbl 1291.65291 J. Comput. Appl. Math. 255, 28-43 (2014). MSC: 65M30 65M70 35R11 26A33 PDFBibTeX XMLCite \textit{M. Li} et al., J. Comput. Appl. Math. 255, 28--43 (2014; Zbl 1291.65291) Full Text: DOI
Xiong, Xiangtuan; Li, Ming; Wang, M. Q. A one-stage meshless method for nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients. (English) Zbl 1367.65156 J. Eng. Math. 80, 189-200 (2013). MSC: 65N20 65N80 35R30 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Eng. Math. 80, 189--200 (2013; Zbl 1367.65156) Full Text: DOI
Xiong, X. T.; Hon, Y. C. Regularization error analysis on a one-dimensional inverse heat conduction problem in multilayer domain. (English) Zbl 1308.65161 Inverse Probl. Sci. Eng. 21, No. 5, 865-887 (2013). MSC: 65M32 35K20 35R25 35R30 PDFBibTeX XMLCite \textit{X. T. Xiong} and \textit{Y. C. Hon}, Inverse Probl. Sci. Eng. 21, No. 5, 865--887 (2013; Zbl 1308.65161) Full Text: DOI
Shi, Wanxia; Xiong, Xiangtuan The Fourier regularization method for inverse heat conduction problem in a multilayer medium. (Chinese. English summary) Zbl 1289.65217 Commun. Appl. Math. Comput. 26, No. 3, 348-354 (2012). MSC: 65M32 65M30 65T50 35K05 35R25 35R30 65M15 PDFBibTeX XMLCite \textit{W. Shi} and \textit{X. Xiong}, Commun. Appl. Math. Comput. 26, No. 3, 348--354 (2012; Zbl 1289.65217)
Li, Ming; Xiong, Xiangtuan On a fractional backward heat conduction problem: application to deblurring. (English) Zbl 1268.65127 Comput. Math. Appl. 64, No. 8, 2594-2602 (2012). MSC: 65M30 35R11 94A08 45K05 PDFBibTeX XMLCite \textit{M. Li} and \textit{X. Xiong}, Comput. Math. Appl. 64, No. 8, 2594--2602 (2012; Zbl 1268.65127) Full Text: DOI
Xiong, Xiangtuan; Guo, Hongbo; Liu, Xiaohong An inverse problem for a fractional diffusion equation. (English) Zbl 1247.65127 J. Comput. Appl. Math. 236, No. 17, 4474-4484 (2012). MSC: 65M32 35K05 35R11 65M12 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Comput. Appl. Math. 236, No. 17, 4474--4484 (2012; Zbl 1247.65127) Full Text: DOI
Xiong, Xiangtuan; Zhou, Qian; Hon, Y. C. An inverse problem for fractional diffusion equation in 2-dimensional case: stability analysis and regularization. (English) Zbl 1245.35144 J. Math. Anal. Appl. 393, No. 1, 185-199 (2012). MSC: 35R11 35R25 35B35 35R30 PDFBibTeX XMLCite \textit{X. Xiong} et al., J. Math. Anal. Appl. 393, No. 1, 185--199 (2012; Zbl 1245.35144) Full Text: DOI
Xiong, X. T.; Wang, J. X.; Li, M. An optimal method for fractional heat conduction problem backward in time. (English) Zbl 1238.35179 Appl. Anal. 91, No. 4, 823-840 (2012). MSC: 35R25 47A52 PDFBibTeX XMLCite \textit{X. T. Xiong} et al., Appl. Anal. 91, No. 4, 823--840 (2012; Zbl 1238.35179) Full Text: DOI
Xiong, Xiangtuan; Wang, Junxia A Tikhonov-type method for solving a multidimensional inverse heat source problem in an unbounded domain. (English) Zbl 1275.65058 J. Comput. Appl. Math. 236, No. 7, 1766-1774 (2012). MSC: 65M32 65M30 35K05 35R25 35R30 65M12 65M15 PDFBibTeX XMLCite \textit{X. Xiong} and \textit{J. Wang}, J. Comput. Appl. Math. 236, No. 7, 1766--1774 (2012; Zbl 1275.65058) Full Text: DOI
Xiong, Xiang-Tuan; Liu, Xiao-Hong; Yan, Yao-Mei; Guo, Hong-Bo A numerical method for identifying heat transfer coefficient. (English) Zbl 1193.80029 Appl. Math. Modelling 34, No. 7, 1930-1938 (2010). MSC: 80M25 35R30 65M32 PDFBibTeX XMLCite \textit{X.-T. Xiong} et al., Appl. Math. Modelling 34, No. 7, 1930--1938 (2010; Zbl 1193.80029) Full Text: DOI
Xiong, Xiang-Tuan On a radially symmetric inverse heat conduction problem. (English) Zbl 1185.35338 Appl. Math. Modelling 34, No. 2, 520-529 (2010). MSC: 35R30 35K20 80A20 PDFBibTeX XMLCite \textit{X.-T. Xiong}, Appl. Math. Modelling 34, No. 2, 520--529 (2010; Zbl 1185.35338) Full Text: DOI
Qian, Ai-Lin; Xiong, Xiang-Tuan; Wu, Yu-Jiang On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation. (English) Zbl 1185.65171 J. Comput. Appl. Math. 233, No. 8, 1969-1979 (2010). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M30 35J05 65M12 35R25 PDFBibTeX XMLCite \textit{A.-L. Qian} et al., J. Comput. Appl. Math. 233, No. 8, 1969--1979 (2010; Zbl 1185.65171) Full Text: DOI
Xiong, Xiang-Tuan A regularization method for a Cauchy problem of the Helmholtz equation. (English) Zbl 1186.65127 J. Comput. Appl. Math. 233, No. 8, 1723-1732 (2010). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M30 35J05 65M12 35R25 PDFBibTeX XMLCite \textit{X.-T. Xiong}, J. Comput. Appl. Math. 233, No. 8, 1723--1732 (2010; Zbl 1186.65127) Full Text: DOI
Li, Hongfang; Fu, Chuli; Xiong, Xiangtuan; Nan, Nan An optimal filtering method for solving a sideways parabolic equation. (Chinese. English summary) Zbl 1212.35183 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 2, 245-252 (2009). MSC: 35K05 35R25 47A52 35R30 PDFBibTeX XMLCite \textit{H. Li} et al., Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 2, 245--252 (2009; Zbl 1212.35183)
Gao, Xiang; Fu, Chuli; Qian, Zhi; Xiong, Xiangtuan; Yan, Liang Optimal filtering regularization method for a non-standard backward heat equation. (Chinese. English summary) Zbl 1164.35523 Chin. J. Eng. Math. 25, No. 1, 35-43 (2008). MSC: 35R25 47A52 35R30 PDFBibTeX XMLCite \textit{X. Gao} et al., Chin. J. Eng. Math. 25, No. 1, 35--43 (2008; Zbl 1164.35523)
Xiong, Xiang-Tuan; Fu, Chu-Li A spectral regularization method for solving surface heat flux on a general sideways parabolic. (English) Zbl 1140.65065 Appl. Math. Comput. 197, No. 1, 358-365 (2008). Reviewer: Aniket Mahanti (Saint John) MSC: 65M30 35K05 35R25 PDFBibTeX XMLCite \textit{X.-T. Xiong} and \textit{C.-L. Fu}, Appl. Math. Comput. 197, No. 1, 358--365 (2008; Zbl 1140.65065) Full Text: DOI
Qian, Z.; Fu, C.-L.; Xiong, X.-T. A modified method for determining the surface heat flux of IHCP. (English) Zbl 1202.80017 Inverse Probl. Sci. Eng. 15, No. 3, 249-265 (2007). MSC: 80A23 80A20 35R30 PDFBibTeX XMLCite \textit{Z. Qian} et al., Inverse Probl. Sci. Eng. 15, No. 3, 249--265 (2007; Zbl 1202.80017) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li Two approximate methods of a Cauchy problem for the Helmholtz equation. (English) Zbl 1182.35237 Comput. Appl. Math. 26, No. 2, 285-307 (2007). MSC: 35R30 35R25 65J20 PDFBibTeX XMLCite \textit{X.-T. Xiong} and \textit{C.-L. Fu}, Comput. Appl. Math. 26, No. 2, 285--307 (2007; Zbl 1182.35237) Full Text: Link
Xiong, Xiang-Tuan; Fu, Chu-Li Error estimates on a backward heat equation by a wavelet dual least squares method. (English) Zbl 1154.65069 Int. J. Wavelets Multiresolut. Inf. Process. 5, No. 3, 389-397 (2007). Reviewer: Fernando Casas (Castellon) MSC: 65M15 65T60 35R25 35K05 65M30 65M60 PDFBibTeX XMLCite \textit{X.-T. Xiong} and \textit{C.-L. Fu}, Int. J. Wavelets Multiresolut. Inf. Process. 5, No. 3, 389--397 (2007; Zbl 1154.65069) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li; Qian, Zhi On three spectral regularization methods for a backward heat conduction problem. (English) Zbl 1132.35494 J. Korean Math. Soc. 44, No. 6, 1281-1290 (2007). MSC: 35R25 35R30 35K05 PDFBibTeX XMLCite \textit{X.-T. Xiong} et al., J. Korean Math. Soc. 44, No. 6, 1281--1290 (2007; Zbl 1132.35494) Full Text: DOI
Fu, Chu-Li; Xiong, Xiang-Tuan; Qian, Zhi Fourier regularization for a backward heat equation. (English) Zbl 1146.35420 J. Math. Anal. Appl. 331, No. 1, 472-480 (2007). MSC: 35R30 35R25 65M32 65M70 80M25 PDFBibTeX XMLCite \textit{C.-L. Fu} et al., J. Math. Anal. Appl. 331, No. 1, 472--480 (2007; Zbl 1146.35420) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li Determining surface temperature and heat flux by a wavelet dual least squares method. (English) Zbl 1113.65096 J. Comput. Appl. Math. 201, No. 1, 198-207 (2007). Reviewer: Tzvetan Semerdjiev (Sofia) MSC: 65M60 65T60 35K05 65M30 35R25 65M15 PDFBibTeX XMLCite \textit{X.-T. Xiong} and \textit{C.-L. Fu}, J. Comput. Appl. Math. 201, No. 1, 198--207 (2007; Zbl 1113.65096) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li Central difference regularization method for the Cauchy problem of the Laplace’s equation. (English) Zbl 1148.65314 Appl. Math. Comput. 181, No. 1, 675-684 (2006). MSC: 65M06 35J05 35R25 65M30 PDFBibTeX XMLCite \textit{X.-T. Xiong} and \textit{C.-L. Fu}, Appl. Math. Comput. 181, No. 1, 675--684 (2006; Zbl 1148.65314) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li; Qian, Zhi; Gao, Xiang Error estimates of a difference approximation method for a backward heat conduction problem. (English) Zbl 1131.65082 Int. J. Math. Math. Sci. 2006, No. 2, Article ID 45489, 9 p. (2006). MSC: 65M30 65M06 65M15 35K05 35R25 PDFBibTeX XMLCite \textit{X.-T. Xiong} et al., Int. J. Math. Math. Sci. 2006, No. 2, Article ID 45489, 9 p. (2006; Zbl 1131.65082) Full Text: DOI EuDML
Qian, Zhi; Fu, Chu-Li; Xiong, Xiang-Tuan A modified method for a non-standard inverse heat conduction problem. (English) Zbl 1105.65097 Appl. Math. Comput. 180, No. 2, 453-468 (2006). Reviewer: Daniel Lesnic (Leeds) MSC: 65M32 35K05 35R30 65M15 PDFBibTeX XMLCite \textit{Z. Qian} et al., Appl. Math. Comput. 180, No. 2, 453--468 (2006; Zbl 1105.65097) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li; Qian, Zhi Two numerical methods for solving a backward heat conduction problem. (English) Zbl 1102.65098 Appl. Math. Comput. 179, No. 1, 370-377 (2006). Reviewer: Daniel Lesnic (Leeds) MSC: 65M32 35K05 35R30 65M06 65M12 PDFBibTeX XMLCite \textit{X.-T. Xiong} et al., Appl. Math. Comput. 179, No. 1, 370--377 (2006; Zbl 1102.65098) Full Text: DOI
Qian, Zhi; Fu, Chu-Li; Xiong, Xiang-Tuan Fourth-order modified method for the Cauchy problem for the Laplace equation. (English) Zbl 1093.65107 J. Comput. Appl. Math. 192, No. 2, 205-218 (2006). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N15 35J05 35R25 PDFBibTeX XMLCite \textit{Z. Qian} et al., J. Comput. Appl. Math. 192, No. 2, 205--218 (2006; Zbl 1093.65107) Full Text: DOI
Xiong, Xiang-Tuan; Fu, Chu-Li; Li, Hong-Fang Fourier regularization method of a sideways heat equation for determining surface heat flux. (English) Zbl 1124.65083 J. Math. Anal. Appl. 317, No. 1, 331-348 (2006). Reviewer: K. N. Shukla (Coimbatore) MSC: 65M32 35R30 65M30 35R25 35K05 65M15 65M12 PDFBibTeX XMLCite \textit{X.-T. Xiong} et al., J. Math. Anal. Appl. 317, No. 1, 331--348 (2006; Zbl 1124.65083) Full Text: DOI
Li, Hong-Fang; Fu, Chu-Li; Xiong, Xiang-Tuan Optimal error bound in a Sobolev space of regularized approximation solutions for a sideways parabolic equation. (English) Zbl 1144.35472 Appl. Math. Mech., Engl. Ed. 26, No. 9, 1238-1244 (2005). MSC: 35R25 80A23 PDFBibTeX XMLCite \textit{H.-F. Li} et al., Appl. Math. Mech., Engl. Ed. 26, No. 9, 1238--1244 (2005; Zbl 1144.35472) Full Text: DOI
Fu, Chuli; Xiong, Xiangtuan; Li, Hongfang Fourier regularization for determining surface heat flux from interior observation based on a sideways parabolic equation. (English) Zbl 1155.65375 Numer. Math., J. Chin. Univ. 14, No. 3, 208-216 (2005). MSC: 65M32 35K05 35R25 35R30 65M15 PDFBibTeX XMLCite \textit{C. Fu} et al., Numer. Math., J. Chin. Univ. 14, No. 3, 208--216 (2005; Zbl 1155.65375)
Fu, Chu-Li; Xiong, Xiang-Tuan; Fu, Peng Fourier regularization method for solving the surface heat flux from interior observations. (English) Zbl 1122.80016 Math. Comput. Modelling 42, No. 5-6, 489-498 (2005). MSC: 80M25 65M70 35R25 80A23 35R30 PDFBibTeX XMLCite \textit{C.-L. Fu} et al., Math. Comput. Modelling 42, No. 5--6, 489--498 (2005; Zbl 1122.80016) Full Text: DOI
Qian, Zhi; Fu, Chu-Li; Xiong, Xiang-Tuan Semidiscrete central difference method in time for determining surface temperatures. (English) Zbl 1079.35101 Int. J. Math. Math. Sci. 2005, No. 3, 393-400 (2005). MSC: 35R30 65N21 PDFBibTeX XMLCite \textit{Z. Qian} et al., Int. J. Math. Math. Sci. 2005, No. 3, 393--400 (2005; Zbl 1079.35101) Full Text: DOI EuDML
Fu, Peng; Fu, Chu-Li; Xiong, Xiang-Tuan; Li, Hong-Fang Two regularization methods and the order optimal error estimates for a sideways parabolic equation. (English) Zbl 1077.80005 Comput. Math. Appl. 49, No. 5-6, 777-788 (2005). Reviewer: D. Lesnic (Leeds) MSC: 80A23 35R25 65M30 35K20 80M25 PDFBibTeX XMLCite \textit{P. Fu} et al., Comput. Math. Appl. 49, No. 5--6, 777--788 (2005; Zbl 1077.80005) Full Text: DOI
Fu, Chuli; Xiong, Xiangtuan; Li, Hongfang; Zhu, Youbin Wavelet and spectral regularization methods for a sideways parabolic equation. (English) Zbl 1068.65116 Appl. Math. Comput. 160, No. 3, 881-908 (2005). Reviewer: Zhang Wanguo (Shanghai) MSC: 65M30 65M70 35R25 35K15 65M15 65T60 PDFBibTeX XMLCite \textit{C. Fu} et al., Appl. Math. Comput. 160, No. 3, 881--908 (2005; Zbl 1068.65116) Full Text: DOI
Fu, Chuli; Xiong, Xiangtuan; Li, Hongfang A Fourier regularization method with Hölder stability for a sideways parabolic equation. (English) Zbl 1089.35550 J. Lanzhou Univ., Nat. Sci. 40, No. 2, 5-7 (2004). MSC: 35R30 47A52 35K05 PDFBibTeX XMLCite \textit{C. Fu} et al., J. Lanzhou Univ., Nat. Sci. 40, No. 2, 5--7 (2004; Zbl 1089.35550)
Xiong, Xiangtuan; Fu, Chuli; Li, Hongfang Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem. (English) Zbl 1068.65117 Appl. Math. Comput. 157, No. 1, 77-91 (2004). Reviewer: Zhang Wanguo (Shanghai) MSC: 65M32 65M06 35K05 35R30 PDFBibTeX XMLCite \textit{X. Xiong} et al., Appl. Math. Comput. 157, No. 1, 77--91 (2004; Zbl 1068.65117) Full Text: DOI