Sixth and fourth order compact finite difference schemes for two and three dimension poisson equation with two methods to derive these schemes

Abstract EN

In this paper we improve the accuracy of the numerical approximation used to solve the two and three dimension Poisson equation.

We get this improvement by using the compact finite difference schemes.

These schemes give high order accuracy ; therefore we derive five schemes to solve two and three dimension Poisson equation : central finite difference, fourth and sixth order compact finite difference by using Taylor expansion scheme, fourth and sixth order compact finite difference by using compact operators scheme.

Numerical experiments are conducted to test accuracy of these schemes.