The approximate solutions of linear Goursat Problems via Homotopy Analysis Method

In this study we investigate the linear Goursat problems that arise in linear partial di¤erential equa- tions with mixed derivatives. The standart form of Goursat Problem is given by uxt = f(x; t; u; ux; ut); 0 6 x 6 a; 0 6 t 6 b; u (x; 0) = g(x); u(0; t) = h(t); u(0; 0) = g(0) = h(0): The aim of this work is to present an e¢ cient numerical procedure, namely Homotopy Analysis Method, for solving homogeneous and inhomogeneous linear Goursat problems. The reliability and e¢ ciency of the proposed method are demonstrated by some numerical examples and performed on the computer algebraic system Mathematica 7.