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Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation. (English) Zbl 07496466

Summary: In this paper, the orthogonal collocation technique with septic Hermite splines as basis function is used to find the numerical solution of non-linear modified Burgers’ equation. The non-linear term appearing in the equation is quasilinearized and then the Crank-Nicolson scheme is used for temporal domain and septic Hermite splines are used for spatial domain discretization. Von-Neumann analysis is used to examine the stability of the technique. The convergence analysis has been done and the proposed method is sixth-order convergent in space and second-order in time. Peano’s theorem is used to estimate the error bounds for septic Hermite interpolation polynomials and all the calculations are performed using Mathematica. The present technique has been tested using three examples. The \(L_2\) and \(L_{\infty}\) norms are computed and are compared with previous work. Present results are found to be better even for less number of mesh points in space and time domains.

MSC:

65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Software:

Mathematica
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Full Text: DOI

References:

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