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

Pramod Kumar Pandey^1,2

¹Department of Mathematics, Dyal Singh College (Univ. of Delhi), New Delhi, India.
²Present Address: Department of Information Technology, College of Applied Sciences, Ministry of Higher Education, Salalah, Sultanate of Oman.

DOI: 10.4236/oalib.1100537                

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 examples validate the efficiency, expected order and accuracy of the method.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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