New integral equation approach to solution of diffusion equation - Sladek, Vladimίr; Sladek, Ján; Keer, Roger van (Computer Assisted Methods in Engineering and Science, 2023)
The paper concerns the theoretical derivation of a new formulation for solution of the initial-boundary value problems for the diffusion equation. The global and local integral equations are derived by using the fundamental solution for the Laplace differential operator. Assuming certain approximations with respect to spatial variable, we obtain a set of the ordinary differential equations (ODE) with continuous time variable. Standard methods for the time integration can be applied to these ODEs. Besides a review of the one step 0-method we propose a new integral equation method for solution of a set of linear ODEs. The paper deals also with the numerical implementation of the global and local integral equations yielding the ODEs.