The Explicit Solution for The Parabolic Equation

Abstract

#Milne applied 11-points formula in irregular domain to approximate the solution of Parabolic equation, But this method is complicated in application. Others [1], [4], applied 5-points formula which is simpler methods but with considerable errors. However, in this work an optimal method has been used nine points formula of Laplace operator in irregular domain which is considerably simple method in comparison with Milne's method and has a good approximation with respect to the analytical solution.