The convergence of two Newton-like methods for solving block nonlinear equations and a class of \(r\)-point \((r+1)\)st-order \(A\)-stable one-block methods

DOI10.1016/S0168-9274(97)00046-9zbMath0885.65072MaRDI QIDQ1369214

Changyin Wang, Shuangsuo Zhao, Guo-Feng Zhang

Publication date: 20 April 1998

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

zbMATH Keywords

convergencenumerical testsparallel computationNewton-like method\(A\)-stabilityblock nonlinear equationsone-block methodssiff systems

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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) Multiple scale methods for ordinary differential equations (34E13)

Related Items

Stability of implicit one-block methods for delay differential equations, An efficient implementation scheme of the simplified Newton iteration for block systems of nonlinear equations

Cites Work

• Parallel step-by-step methods
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• The solution of a combustion problem with Rosenbrock methods
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• The stability of the block θ-methods
• Comparing numerical methods for stiff systems of O.D.E:s
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• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems
• The automatic integration of ordinary differential equations
• A-stable block implicit one-step methods
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