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Stable numerical solutions preserving qualitative properties of nonlocal biological dynamic problems. (English) Zbl 1474.65286

Summary: This paper deals with solving numerically partial integrodifferential equations appearing in biological dynamics models when nonlocal interaction phenomenon is considered. An explicit finite difference scheme is proposed to get a numerical solution preserving qualitative properties of the solution. Gauss quadrature rules are used for the computation of the integral part of the equation taking advantage of its accuracy and low computational cost. Numerical analysis including consistency, stability, and positivity is included as well as numerical examples illustrating the efficiency of the proposed method.

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
92B05 General biology and biomathematics
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