A Novel Study Based on Lerch Polynomials for Approximate Solutions of Pure Neumann Problem
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Date
2022
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Abstract
The Neumann problem is used to model many linear and nonlinear phenomena such as electrostatic problems, acoustic problems, vibrations of a string, fluid flow problems, the evolution of an isolated population, etc. This paper proposes a numerical technique to solve second-order linear partial differential equations with variable coefficients subject to the Neumann boundary condition (i.e., the boundary condition of the second kind). Our technique uses the operational matrix method and standard collocation points and approximates the solution using Lerch polynomials bases. Also, we enhance the method's effectiveness by utilizing an error analysis technique based on residual function. The implementation of our method to any computer program is more straightforward than many other numerical methods. The results of numerical experiments are illustrated with tables and figures and are compared with analytical solutions to confirm the good accuracy of the presented technique. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.