A-stable one-step methods with step-size control for stiff systems of ordinary differential equations

DOI10.1016/0771-050X(78)90016-5zbMath0386.65035MaRDI QIDQ1249838

Rene Alt

Publication date: 1978

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

Related Items (17)

The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations ⋮ An embedded 3(2) pair of nonlinear methods for solving first order initial-value ordinary differential systems ⋮ A family of embedded Runge-Kutta formulae ⋮ Haar wavelet approach to linear stiff systems. ⋮ Analysis of trajectory errors in integrating ordinary differential equations ⋮ The numerical simulation for stiff systems of ordinary differential equations ⋮ Solving first-order initial-value problems by using an explicit non-standard \(A\)-stable one-step method in variable step-size formulation ⋮ A tenth order \(\mathcal{A} \)-stable two-step hybrid block method for solving initial value problems of ODEs ⋮ A NEW SUPERCLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS ⋮ Wavelet approach incorporated with optimization for solving stiff systems ⋮ Error estimators for stiff differential equations ⋮ Analysis of stiff systems via method of shifted Jacobi functions ⋮ A new family of A-stable Runge-Kutta methods with equation-dependent coefficients for stiff problems ⋮ Analysis of stiff systems via the method of generalized orthogonal polynomials ⋮ Analysis of stiff systems via single step method of block pulse functions ⋮ A modified group-preserving scheme for solving the initial value problems of stiff ordinary differential equations ⋮ Analysis of stiff systems via method of shifted Legendre functions

Cites Work

• Some results in the theory of the vector \(\varepsilon\)-algorithm
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• Exponentially fitted multistep methods by generalized Hermite-Birkhoff interpolation
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• High order a-stable methods for the numerical solution of systems of D.E.'s
• Implicit integration processes with error estimate for the numerical solution of differential equations
• A class ofA-stable methods
• The automatic integration of ordinary differential equations
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
• A-stable block implicit one-step methods
• A -Stable Composite Multistep Methods
• Implicit Runge-Kutta Processes
• A special stability problem for linear multistep methods
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