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A Finite Difference Method for Numerical Solution of Goursat Problem of Partial Differential Equation

DOI: 10.4236/oalib.1100537, PP. 1-6

Subject Areas: Numerical Mathematics, Ordinary Differential Equation

Keywords: Numerical Method, Finite Difference Method, Goursat Problem, Maximum Absolute Error, Relative Error, Root Mean Square Error, Nonlinear Problem

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Abstract

In this article, we report the finite difference method for numerically solving the Goursat Problem, using uniform Cartesian grids on the square region. We have considered both linear and nonlinear Goursat problems of partial differential equations for the numerical solution, to ensure the accuracy of the developed method .The results obtained for these numerical examplesvalidate the eciency, expected order and accuracy of the method.

Cite this paper

Pandey, P. K. (2014). A Finite Difference Method for Numerical Solution of Goursat Problem of Partial Differential Equation. Open Access Library Journal, 1, e537. doi: http://dx.doi.org/10.4236/oalib.1100537.

References

[1]  Day, J.T. (1966) Runge-Kutta Method for the Numerical Solution of the Goursat Problem in Hyperbolic Partial Differential Equations. Computer Journal, 9, 81-83.
http://dx.doi.org/10.1093/comjnl/9.1.81
[2]  Jain, M.K. and Sharma, K.D. (1968) Cubature Method for the Numerical Solution of the Characteristic Initial Value Problems, . Journal of the Australian Mathematical Society, 8, 355-368.
http://dx.doi.org/10.1017/S1446788700005425
[3]  Evans, D.J. and Sanugi, B.B. (1988) Numerical Solution of the Goursat Problem by a Nonlinear Trapezoidal Formula. Applied Mathematics Letters, 1, 221-223.
http://dx.doi.org/10.1016/0893-9659(88)90080-8
[4]  Stetter, H.J. and Torning, W. (1963) General Multistep Finite Difference Method for the Solution of . Rendiconti del Circolo Matematico di Palermo, 12, 281-298.
http://dx.doi.org/10.1007/BF02851264
[5]  Nasir, M.A.S. and Ismail, A.I.M. (2005) A New Finite Difference Scheme Based on Heronian Mean Averaging for the Goursat Problem. ISAME Transactions, 2, 98-103.
[6]  Jeffrey, A. and Taniuti T. (1964) Nonlinear Wave Propagation. Academic Press, New York.
[7]  Pandey, P.K. (2014) A Fourth Order Finite Difference Method for the Goursat Problem. Acta Technica Jaurinensis, 7, 319-327.
[8]  Chawla, M.M. (1979) A Sixth Order Tridiagonal Finite Difference Method for General Nonlinear Two Point Boundary Value Problems. Journal of the Institute of Mathematics and its Applications, 24, 35-42.
http://dx.doi.org/10.1093/imamat/24.1.35

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