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- W343131645 abstract "A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nikolson scheme for the numerical solution of the one-dimensional heat equation. Numerical examples are given for both Neumann and Dirichlet initial boundary value problems. The fourth-order methods proposed are compared with high-order compact schemes. The set of methods proposed demonstrate a better performance compared with high-order compact schemes in the case of the Neumann boundary conditions. Index Terms—high-order difference scheme; deferred correc- tion scheme; high-order compact scheme; heat equation. HE desired properties of finite difference schemes are stability, accuracy and efficiency. These requirements are in conflict with each other. In many applications a high- order accuracy is required in the spatial discretization. To reach better stability, implicit approximation is desired. For a high-order method of traditional type (not a high-order compact (HOC)), the stencil becomes wider with increasing order of accuracy. For a standard centered discretization of order p, the stencil is p+1 points wide. This inflicts problems at the fictional boundaries, and using an implicit method results in the solution of an algebraic system of equations with large bandwidth. In light of conflict requirements of stability, accuracy and computational efficiency, it is desired to develop schemes that have a wide range of stability, high- order of accuracy and lead to the solution of the system of linear equations with a tridiagonal matrix, i.e. the system of linear equations arising from a standard second order discretization of heat equation. The development of high order compact schemes (HOC)" @default.
- W343131645 created "2016-06-24" @default.
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- W343131645 date "2013-01-01" @default.
- W343131645 modified "2023-09-27" @default.
- W343131645 title "Deferred Correction Technique to Construct High-Order Schemes for the Heat Equation with Dirichlet and Neumann Boundary Conditions" @default.
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