AbstractA new multidomain direct (noniterative) method for solving boundary‐value problems is presented. Using this method, the solution is expressed by a linear combination of auxiliary functions and unknowns which pertain to the boundaries of a subdomain. This approach enables us to solve problems independently and exactly, without any iterations between subdomains. As a consequence, different types of equations and coordinate systems may be considered in different subdomains. Moreover, different boundary conditions and variable (in space) time steps may be imposed on the subdomains as well. Applications are given for initial boundary‐value problems with known analytical solutions, including a highly nonlinear porosity equation. © 1994 John Wiley&Sons,