2021
DOI: 10.4208/cicp.oa-2019-0197
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A Kernel Based Unconditionally Stable Scheme for Nonlinear Parabolic Partial Differential Equations

Abstract: In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [11] for convection-diffusion equations, which relies on a special kernel-based formulation of the solutions and successive convolution. However, disadvantages appear when we extend the previous method to our equations, such as inefficient choice of parameters and unprovable stability for high-dimensional problems. To overcome these … Show more

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