Armstrong, Seth; Brown, Sarah; Han, Jianlong Numerical analysis for a nonlocal phase field system. (English) Zbl 1337.65114 Int. J. Numer. Anal. Model., Ser. B 1, No. 1, 1-19 (2010). Summary: We propose a stable, convergent finite difference scheme to solve numerically a nonlocal phase field system which may model a variety of nonisothermal phase separations in pure materials which can assume two different phases, say solid and liquid, with properties varying in space. The scheme inherits the characteristic property of conservation of internal energy. We also prove that the scheme is uniquely solvable and the numerical solution will approach the true solution in the \(L^\infty \)-norm. Cited in 5 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 45K05 Integro-partial differential equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 74N99 Phase transformations in solids 80A22 Stefan problems, phase changes, etc. Keywords:finite difference scheme; nonisothermal; long-range interaction PDFBibTeX XMLCite \textit{S. Armstrong} et al., Int. J. Numer. Anal. Model., Ser. B 1, No. 1, 1--19 (2010; Zbl 1337.65114)