A second order accurate difference scheme for the heat equation with concentrated capacity

Summary. A numerical solution to the one-dimensional heat equation with concentrated capacity is considered. A second-order accurate difference scheme is derived by the method of reduction of order on non-uniform meshes. The solvability, stability and second order L convergence are proved. A numerical example demonstrates the theoretical results.Mathematics Subject Classification (2000): Primary 65M06, 65M12, 65M15The contract grant sponsor: National Natural Science Foundation of CHINA; The contract grant number:19801007