On the lack of convergence of unconditionally stable explicit rational Runge-Kutta schemes

DOI10.1016/0045-7825(86)90011-3zbMath0611.65057OpenAlexW1993847096MaRDI QIDQ1087319

Jean H. Prévost, Anthony P. Peirce

Publication date: 1986

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(86)90011-3

zbMATH Keywords

consistencyunconditional stabilityrational Runge-Kutta methodstime- integration schemes

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Mechanics of continuous porous media

Cites Work

• Unnamed Item
• On a deficiency in unconditionally stable explicit time-integration methods in elastodynamics and heat transfer
• New stability theorems concerning one-step numerical methods for ordinary differential equations
• Unconditionally stable explicit methods for parabolic equations
• Partial differential equations. 4th ed
• Rational Runge-Kutta methods for solving systems of ordinary differential equations
• Survey of the stability of linear finite difference equations
• Partitioned rational Runge Kutta for parabolic systems
• Nonlinear stability ofRAT, an explicit rational Runge-Kutta method
• Unconditionally stable implicit-explicit algorithms for coupled thermal stress waves