Geodesic
On iterative solution of nonlinear heat-conduction and diffusion problems
Applications of Mathematics, Tome 22 (1977) no. 2, pp. 77-91
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The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
DOI : 10.21136/AM.1977.103680
Classification : 35A35, 35D05, 35K55, 47H15, 65N22, 65N30
Keywords: diffusion problems; iterative solution; Banach fixed-point theorem; nonlinear heat-conduction; generalized Sobolev spaces of vector valued function 
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Gajewski, Herbert. On iterative solution of nonlinear heat-conduction and diffusion problems. Applications of Mathematics, Tome 22 (1977) no. 2, pp. 77-91. doi: 10.21136/AM.1977.103680

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