Applied Numerical Mathematics 47 (2003) 467–476 www.elsevier.com/locate/apnum Accurate numerical solution of coupled time dependent parabolic initial value problems ✩ L. Jódar a,∗ , J.I. Castaño b , J.A. Sánchez b , G. Rubio a a Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Valencia, Spain b Departamento de Ciencias Básicas, Universidad Eafit, Medellín, Colombia Abstract This paper deals with the construction of numerical solutions with a prefixed accuracy of initial value problem for coupled time dependent initial value problems using Fourier transform, numerical integration and numerical resolution of differential equations. An algorithm is included.  2003 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Coupled parabolic system; Fourier transform; Initial value problem 1. Introduction Coupled parabolic partial differential systems are frequently found in the study of heat conduction and diffusion problems [1,2]. In the evaluation of coupled microwave heating processes the constant coefficient model often leads to misleading results due to complexity of the field distribution within the oven and the variation in dielectric properties of material with temperature, moisture content, density and other properties [1,2]. In this paper we consider initial value problems of the form u t = B(t)u xx + A(t)u x + C(t)u, -∞ <x< ∞,t> 0, (1) u(x, 0) = f(x), -∞ <x< ∞, (2) ✩ This paper has been supported by the Generalitat Valenciana and Spanish Grant DPI 2001-2703-C02-02 and Colciencias- BID Colombian. * Corresponding author. E-mail addresses: ljodar@mat.upv.es (L. Jódar), icastano@eafit.edu.co (J.I. Castaño), josanche@eafit.edu.co (J.A. Sánchez), grubio@mat.upv.es (G. Rubio). 0168-9274/$30.00  2003 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/S0168-9274(03)00086-2