Convergence of meshfree collocation methods for fully nonlinear parabolic equations

2014/08/22 by Yumiharu Nakano, Nakano, Yumiharu
Engineering · Mathematics · #Numerical methods in engineering #Fractional Differential Equations Solutions #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1408.5195

Abstract

We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the framework of viscosity solutions, provided that the basis function approximations of the terminal condition and the nonlinearities are successful at each time step. A numerical experiment with a radial basis function demonstrates the convergence property.

Citations

• Semi-Lagrangian Schemes for Linear and Fully Non-Linear Diffustion Equations

Related

• Convergence of differentiable non-monotone schemes for fully nonlinear parabolic equations
• Convergence of Rothe's method for fully nonlinear parabolic equations
• On Convergence of Solutions to Equilibria for Fully Nonlinear Parabolic\n Systems with Nonlinear Boundary Conditions
• A Nonlinear Discretization Theory for Meshfree Collocation Methods applied to Quasilinear Elliptic Equations
• Numerical analysis of strongly nonlinear PDEs