Open Accessthe numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes
Author(s) -
Pramod Kumar Pandey
Publication year - 2021
Publication title -
qubahan academic journal
Language(s) - English
Resource type - Journals
ISSN - 2709-8206
DOI - 10.48161/qaj.v1n1a19
Subject(s) - mathematics , boundary value problem , ordinary differential equation , convergence (economics) , helmholtz equation , finite difference method , variable (mathematics) , order of accuracy , mathematical analysis , finite difference , method of fundamental solutions , numerical analysis , helmholtz free energy , rate of convergence , point (geometry) , partial differential equation , differential equation , finite element method , boundary knot method , numerical partial differential equations , computer science , geometry , boundary element method , key (lock) , physics , quantum mechanics , economics , thermodynamics , economic growth , computer security
In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.