Approximate Solutions of The Cauchy Problem for The Heat Equations

Homotopy Analysis Method (HAM) is applied to the problem of the one-dimensional heat equations with a non-linear heat source subject to the temperature and the heat flux given at a single boundary to obtain the analytical solutions. Solutions obtained take an important place for one-dimensional heat flow as applied to a few regular geometries such as slabs, cylinders and spheres. Some of the test problems are presented to show the efficiency of HAM.