Accurate numerical solution of initial value problems for the time dependent convection-diffusion equation

Abstract By using the Fourier transform method and composite Simpson's integration formula, a symbolically computable approximate solution of an initial value problem for the time dependent convection-diffusion equation is constructed. Given an admissible error e and a point ( x, t ), the approximation constructed with error less than ϵ at ( x, t ) can be symbolically obtained using Mathematics 4.0.