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


  • Liaquat Ali Zardari Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan
  • Shakeel Ahmed Kamboh Department of Mathematics and Statistics, QUEST, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan
  • Abbas Ali Ghoto Department of Mathematics and Statistics, QUEST, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan
  • Dr. Kirshan Kumar Luhana Department of Computer Science, Laar Campus, Sindh University Jamshororo, Pakistan
  • Dr. Shah Zaman Nizamani Department of Information Technology, Quaid-e-Awam University, Pakistan




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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How to Cite

Zardari, L. A., Kamboh, S. A., Ghoto, A. A., Kumar Luhana, D. K., & Nizamani, D. S. Z. (2022). Effect of the Arbitrary Coefficients on the convergence of numerical solution of General Second Order Linear Homogeneous Partial Differential Equation. VFAST Transactions on Mathematics, 10(2), 102–117. https://doi.org/10.21015/vtm.v10i2.1211