A finite difference alternating segment scheme of parallel computations for solving heat equation
نویسندگان
چکیده
In this paper, a numerical scheme named alternating segment Crank-Nikolson is used for solving heat equation. This scheme can be used directly on parallel computations. Truncation error and stability of the presented method is analyzed. Comparison in accuracy with the fully implicit Crank-Nikolson scheme is presented in numerical experiment.
منابع مشابه
High-accuracy alternating segment explicit-implicit method for the fourth-order heat equation
Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...
متن کاملSolving a system of 2D Burgers' equations using Semi-Lagrangian finite difference schemes
In this paper, we aim to generalize semi-Lagrangian finite difference schemes for a system of two-dimensional (2D) Burgers' equations. Our scheme is not limited by the Courant-Friedrichs-Lewy (CFL) condition and therefore we can apply larger step size for the time variable. Proposed schemes can be implemented in parallel very well and in fact, it is a local one-dimensional (LOD) scheme which o...
متن کاملOn a modication of the Chebyshev collocation method for solving fractional diffiusion equation
In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...
متن کاملA Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...
متن کاملA New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...
متن کامل