Numerical Solutions Of The Nonlocal Problems For The Diffusion Partial Differential Equations

Abstract

In this work, we use the explicit and the implicit finite-difference methods to solve the nonlocal problem that consists of the diffusion equations together with nonlocal conditions. The nonlocal conditions for these partial differential equations are approximated by using the composite trapezoidal rule, the composite Simpson's 1/3 and 3/8 rules. Also, some numerical examples are presented to show the efficiency of these methods.

Keywords

• finite difference method, implicit finite difference method, explicit finite difference method, nonlocal condition, diffusion equation.