Residual power series method for solving nonlinear reaction-diffusion-convection problems

where u = u(x, t) is an unknown function, and the arbitrary smooth functions a(u), b(u) and c(u) denote the diffusion term, the convection term and the reaction term respectively. The reaction diffusion convection equations are widely used in many areas in science such as biology modeling, physics, chemistry, astrophysics, medicine and engineering. For example, heat conduction [4], [5] and [20], haemodynamics [9], [23] and [22], dynamics of blood coagulation [6] and [25], cardiac arrhythmias [8] and [24] and atherosclerosis [16] and [15]. The following equation is a special case of the reaction diffusion convection equations, the Murray equation [18] and [19]