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math.AP2017★ 15 cited
Analytic approximation of solutions of parabolic partial differential equations with variable coefficients
Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba
A complete family of solutions for the one-dimensional reaction-diffusion equation \[ u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t) \] with a coefficient depending on is constructed. T…
math.AP2017
Solution of parabolic free boundary problems using transmuted heat polynomials
Igor V. Kravchenko, Vladislav V. Kravchenko, Sergii M. Torba
A numerical method for free boundary problems for the equation \[ u_{xx}-q(x)u=u_t \] is proposed. The method is based on recent results from transmutation operators theory allowin…