A non-separable solution of the diffusion equation based on the Galerkin's method using cubic splines
The authors present an algorithm to solve the two dimensional diffusion equation based on the Galerkin method where a collocation method is applied to the initial condition using bi-cubic \(B\)-splines [cf. \textit{I. Dağ, B. Saka} and \textit{A. Boz}, Appl. Math. Comput. 166, No.~3, 506--522 (2005; Zbl 1073.65099)]. The proposed method is applicable whenever the initial condition is given in an unbounded region or with a free boundary condition. It is shown that for the diffusion equation in an unbounded region, there is a very simple effective solution for the time dependent equation.
scientific article; zbMATH DE number 5817267
scientific article