Effect of the Arbitrary Coefficients on the convergence of numerical solution of General Second Order Linear Homogeneous Partial Differential Equation

Liaquat Ali Zardari, Shakeel Ahmed Kamboh, Abbas Ali Ghoto, Dr. Kirshan Kumar Luhana, Dr. Shah Zaman Nizamani

Abstract


In this study the effect of the coecients on the convergence of numerical solution of general second order linear homogeneous partial differential equation has been investigated. The main objective was to determine the sensitivity of the coecients of the PDE in relation to the domain and mesh size. The nite difference method was used to discretize the PDE and numerical solution was obtained by implementing the algorithm on MATLAB. The outcomes of the research have provided interesting facts about the stable values of the coecients. From the results it is found that the arbitrary coecients d and e are more sensitive as compared to a, b, c and f. The outcomes of this research study are expected to provide the ways to predict and control the numerical solution convergence behavior obtained by the general second order PDE based on the variable coecients of the PDE.

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DOI: http://dx.doi.org/10.21015/vtm.v10i2.1211

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