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A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method
In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.
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Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...
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 ...
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In this paper, the solution of the evolutionaryfourth-order in space, Sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{HPM}). The results revealthat the method is very effective, convenient and quite accurateto systems of nonlinear partial differential equations.
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In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets. The method combines implicit collocation with the multi-scale method. Using the multi-scale method, SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain. The stability and c...
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