L 0 -stable splitting methods for the simple heat equation in two space dimensions with homogeneous boundary conditions

$L_0 $-stable splitting methods which are third and fourth order accurate in time are developed for the numerical solution of the simple diffusion equation in two space dimensions.The methods are seen to evolve from first and second order Pade approximants to the exponential function. The local truncation errors of the methods are compared and the costs of implementing the algorithms are estimated by arithmetic operations counts.The methods are tested on a constant coefficients problem for which there is a discontintlty between initial conditions and boundary conditions.