Abstract:
A new method for obtaining a generalized solution of a mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition is proposed. Generalized functions are understood in the sense of a sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions of the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.
Keywords:mixed boundary value problem, generalized solution, sinc approximation, uniform convergence.
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