Sixth Order Finite Difference In Two Dimensions With Some Examples (Al-Mansour Journal, 2022)
A nine-points sixth – order accurate compact finite difference method for solving Laplace equation in two dimensional is present. The efficiency of the method is validated by its application to the test problems which have exact solutions. Numerical results show that this sixth order scheme has the expected accuracy. The explicit numerical solution of the parabolic equation is given, In addition, can be applicable to domain with some obstacle, as well, improve the solution of Poisson equation by taking more terms from the right hand side. All the computations are solved by the iterative method with personal computer.
Keywords: Six order finite difference; Laplace equation; parabolic equation; Poisson equation