A New Algorithm that Developed Finite Difference Method for Solving Laplace Equation for a Plate with Four Different Constant Temperature Boundary Conditions

摘要

Solving Laplace equation ▽~2T = 0 using analytical methods is difficult, so numerical methods are used. One of the numerical methods for solving Laplace equation is finite difference method. We know that knotting and writing finite difference method for a specific body, eventually will give rise to linear algebraic equations, In this study, a new algorithm use for develop finite difference method for solving Laplace equation. In this algorithm, the temperature of the nodes of a specific figure quickly will be evaluated using finite difference method and the number of equations would be reducing significantly. By this method, a new formula for solving Laplace equation for a plate with four different constant temperature boundary conditions (Dirichlet condition) derived.