Wang, Li; Zhang, Lin An application of Zakian inversion method in solving hyperbolic differential equations. (Chinese. English summary) Zbl 1299.65251 J. Sichuan Norm. Univ., Nat. Sci. 36, No. 4, 530-533 (2013). Summary: By means of the Laplace transformation, the hyperbolic differential equations are transformed to elliptic differential equations which can be solved by the fourth order finite difference scheme in parallel. After getting the approximate solutions of the elliptic differential equations, we can achieve the numerical solutions with high accuracy in any time for the hyperbolic differential equations by using the Zakian inversion method. At last, we carry out one numerical experiment to indicate that the method in this paper is very effective. MSC: 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65N06 Finite difference methods for boundary value problems involving PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs 44A10 Laplace transform 35L20 Initial-boundary value problems for second-order hyperbolic equations 35J25 Boundary value problems for second-order elliptic equations 65Y05 Parallel numerical computation Keywords:hyperbolic differential equations; Zakian inversion method; finite difference methods; parallel computation; Laplace transformation; elliptic differential equations; numerical experiment PDFBibTeX XMLCite \textit{L. Wang} and \textit{L. Zhang}, J. Sichuan Norm. Univ., Nat. Sci. 36, No. 4, 530--533 (2013; Zbl 1299.65251) Full Text: DOI