Numerical solution of a non-classical parabolic problem: An integro-differential approach

A numerical method based on an integro-differential formulation and approximation by local interpolating functions is proposed for solving a one-dimensional parabolic partial differential equation subject to non-classical conditions. Some specific test problems are solved using the proposed method. Numerical results obtained indicate that it can give accurate solutions and that it is an interesting and viable alternative to existing numerical methods for solving the class of problems under consideration.