Unconditionally stable numerical method for a nonlinear partial integro-differential equation

The paper presents an unconditionally stable numerical scheme to solve a nonlinear integro-differential equation which arises in mathematical modelling of the penetration of a magnetic field into a substance, if the temperature is kept constant throughout the material. Numerical scheme comprises of the Galerkin finite element method [18] for the spatial discretization followed by an implicit finite difference scheme for the time stepping. We extended the results for stability estimates to a nonhomogeneous problem and derived optimal order error estimates for the semidiscretized and fully discretized equations using H 0 projection. Further, to show the efficiency, the proposed numerical method is demonstrated via numerical example.