on the convergence of the homotopy analysis method to solve the system of partial dierential equations

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the approximate solution ofsome systems of pdes. also, we show the region of convergence by plotting the h-surface.