Numerical computation of a nonlocal double obstacle problem. (English) Zbl 1207.65155

Bhowmik, Samir K.

Int. J. Open Probl. Comput. Sci. Math., IJOPCM 2, No. 1, 19-36 (2009).

Summary: We consider a nonlocal double obstacle problem. This type of problems comes in various biological and physical situations, e.g., in phase transition models. We focus on numerical approximations and fast computation of such a model. We start with considering piece-wise basis functions for spatial approximation followed by an implicit Euler’s method for time integration and then Newton’s method for solving the resulting nonlinear system. Then we apply various linear system solver to get a time efficient technique to solve the model. We also attempt Fourier transform in space as well.

MSC:

65R20	Numerical methods for integral equations
45K05	Integro-partial differential equations
45G10	Other nonlinear integral equations
65H10	Numerical computation of solutions to systems of equations

Keywords:

partial integro-differential equation; phase transition models; piecewise constant functions; Matlab; Fourier transforms; Newton’s method; Jacobian; iterative methods; implicit Euler’s method

Software:

Matlab