Analytic-numerical solutions of diffusion mathematical models with delays. (English) Zbl 1155.65387

Summary: This work deals with the construction of analytic-numerical solutions of mixed problems for diffusion and reaction-diffusion equations with delay. Using the method of separation of variables, exact theoretical infinite series solutions are derived. Bounds on the truncation errors, when these series are approximated by finite sums, are given, thus providing constructive continuous numerical solutions with prescribed accuracy in bounded domains. In order to improve the computational efficiency of these numerical solutions, polynomial approximations to the initial functions are also considered.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K57 Reaction-diffusion equations
35C10 Series solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
Full Text: DOI


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