Implementing Second-Derivative Multistep Methods Using the Nordsieck Polynomial Representation

DOI10.2307/2006255zbMath0385.65034OpenAlexW4245587770MaRDI QIDQ4166146

Gopal Gupta

Publication date: 1978

Full work available at URL: https://doi.org/10.2307/2006255

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical integration (65D30)

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Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs ⋮ Third derivative hybrid block integrator for solution of stiff systems of initial value problems ⋮ One step adapted hybrid second derivative block method for initial value problems with oscillating solutions ⋮ A Polynomial Representation of Hybrid Methods for Solving Ordinary Differential Equations ⋮ Second derivative of high-order accuracy methods for the numerical integration of stiff initial value problems ⋮ Block hybrid method using trigonometric basis for initial value problems with oscillating solutions ⋮ A new family of multistep numerical integration methods based on Hermite interpolation ⋮ Solving second order initial value problems by a hybrid multistep method without predictors ⋮ HIGH ORDER SECOND DERIVATIVE DIAGONALLY IMPLICIT MULTISTAGE INTEGRATION METHODS FOR ODES ⋮ A trigonometrically fitted intra-step block Falkner method for the direct integration of second-order delay differential equations with oscillatory solutions ⋮ Unnamed Item ⋮ The efficiency of second derivative multistep methods for the numerical integration of stiff systems

Cites Work

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• On Numerical Integration of Ordinary Differential Equations
• Comparing numerical methods for stiff systems of O.D.E:s
• Note onA-stability of multistep multiderivative methods
• An algebraic approach toA-stable linear multistep-multiderivative integration formulas
• Some New High-Order Multistep Formulae for Solving Stiff Equations
• Exponentially fitted multistep methods by generalized Hermite-Birkhoff interpolation
• A-stable, Accurate Averaging of Multistep Methods for Stiff Differential Equations
• Stable high order implicit methods for the numerical solution of systems of differential equations
• Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
• Multistep Methods with Variable Matrix Coefficients
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
• A special stability problem for linear multistep methods

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