High-Order, Accurate Finite Difference Schemes for Fourth-Order Differential Equations

This article is devoted to the study of high-order, accurate difference schemes' numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical integral transform methods. However, these classical methods can be used simply in the case when the differential equation has constant coefficients. We study fourth-order differential equations with dependent coefficients and their corresponding boundary value problems. Novel compact numerical solutions of high-order, accurate finite difference schemes generated by Taylor's decomposition on five points have been studied in these problems. Numerical experiments support the theoretical statements for the solution of these difference schemes.