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.
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
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
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
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
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.
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