A nonconventional stability approach for a nonlinear Crank-Nicolson method solving degenerate Kawarada problems

DOI10.1016/J.AML.2023.108730OpenAlexW4378673909MaRDI QIDQ6112158

Eduardo Servin Torres, Qin Sheng

Publication date: 7 July 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2023.108730

zbMATH Keywords

stabilityquenchingfinite difference methodsdegeneracyKawarada equations

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Parabolic equations and parabolic systems (35Kxx) Qualitative properties of solutions to partial differential equations (35Bxx)

Cites Work

• Unnamed Item
• Numerical stability in the presence of variable coefficients
• Adaptive moving mesh methods
• Numerical solution of quenching problems using mesh-dependent variable temporal steps
• On solutions of initial -boundary problem for \(u_t=u_{xx}+1/(1-u)\)
• Parabolic quenching for nonsmooth convex domains
• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations
• An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids
• A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation
• A preservative splitting approximation of the solution of a variable coefficient quenching problem
• An energy-preserving Crank-Nicolson Galerkin method for Hamiltonian partial differential equations
• A Liouville theorem for a heat equation and applications for quenching
• Chaos-free numerical solutions of reaction-diffusion equations
• A First Course in the Numerical Analysis of Differential Equations
• Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting
• On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations
• Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems
• Nonuniform Crank‐Nicolson scheme for solving the stochastic Kawarada equation via arbitrary grids
• A Revisit of the Semi-Adaptive Method for Singular Degenerate Reaction-Diffusion Equations

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