Two-level fourth-order explicit schemes for diffusion equations subject to boundary integral specifications

Several processes in the natural sciences and engineering lead to nonclassical parabolic initial boundary value problems with nonlocal boundary conditions. Many authors have studied second-order parabolic equations, particularly the heat equation with this kind of condition. In [19], several methods were compared to approach the numerical solution of the one-dimensional heat equation subject to the specifications of mass. Here, two two-level fourth-order explicit algorithms are derived. They improve the CPU time and accuracy of other explicit and implicit schemes seen with this kind of problems. The convergence of the algorithms is studied and finally, numerical examples are given to compare the efficiency of the new methods with others used for this kind of problem.