The vector form of a sixth-order \(A\)-stable explicit one-step method for stiff problems

DOI10.1016/S0898-1221(99)00349-1zbMath0954.65059MaRDI QIDQ1570146

Jian-Lin Xia, Xin-Yuan Wu

Publication date: 25 January 2001

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

stabilitynumerical experimentsinitial value problemsystem of ordinary differential equationsstiff problemmodified Taylor series method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (16)

One-step explicit methods for the numerical integration of perturbed oscillators ⋮ A two-step explicit \(P\)-stable method of high phase-lag order for linear periodic IVPs ⋮ A two-step explicit \(P\)-stable method for solving second order initial value problems. ⋮ New vector forms of elemental functions with Taylor series. ⋮ Unnamed Item ⋮ A two-step explicit \(P\)-stable method of high phase-lag order for second order IVPs. ⋮ The new class of implicit \(L\)-stable hybrid Obrechkoff method for the numerical solution of first order initial value problems ⋮ A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems ⋮ A class of two-step explicit methods for periodic IVPs ⋮ Study of general Taylor-like explicit methods in solving stiff ordinary differential equations ⋮ Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs ⋮ Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods ⋮ On the stability of a two-step method for solving periodic IVPs ⋮ Novel Padé‐based algorithms for numerical integration of ODEs ⋮ An explicit two-step method exact for the scalar test equation \(y'= \lambda y\) ⋮ Two-step explicit methods for second-order IVPs with oscillatory solutions

Cites Work

• Differential equations and their applications. An introduction to applied mathematics. 3rd ed
• Numerical solution of a quasilinear parabolic problem
• Unconditionally stable explicit methods for parabolic equations
• Rational Runge-Kutta methods for solving systems of ordinary differential equations
• A sixth-order \(A\)-stable explicit one-step method for stiff systems
• Acceleration Techniques for Iterated Vector and Matrix Problems
• The automatic integration of ordinary differential equations
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