1. On an Iterative Method of Solving Direct and Inverse Problems for Parabolic Equations.
- Author
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Boykov, I. V. and Ryazantsev, V. A.
- Subjects
- *
NUMERICAL integration , *NONLINEAR equations , *NONLINEAR operators , *EQUATIONS , *OPERATOR equations , *INVERSE problems - Abstract
This paper is devoted to approximate methods of solving direct and inverse problems for parabolic equations. An approximate method to solve the initial problem of a multidimensional nonlinear parabolic equation has been proposed. It is based on reducing the initial problem to a nonlinear multidimensional Fredholm intergral equation of the second kind, which is approximated by a system of nonlinear algebraic equatiions using a method of mechanical quadratures. In constructing a computational scheme, the points of local splines have been applied for optimal with respect to order approximation of a functional class that contains the solutions of parabolic equations. For the numerical implementation of the computational scheme, we have used the generalization of a continuous method of solving nonlinear operator equations that is described in the paper. In addition, the inverse problem of a parabolic equation with a fractional order derivative with respect to a time variable has been studied. Approximate methods of determining the fractional order of the time derivative and a coefficient at a spatial derivative have been proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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