An algebraic approach toA-stable linear multistep-multiderivative integration formulas

DOI10.1007/BF01932535zbMath0322.65037MaRDI QIDQ4085191

Y. Genin

Publication date: 1974

Published in: BIT (Search for Journal in Brave)

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical analysis in abstract spaces (65J99)

Related Items (11)

Implementing Second-Derivative Multistep Methods Using the Nordsieck Polynomial Representation ⋮ Unnamed Item ⋮ Implicit multiderivative collocation solvers for linear partial differential equations with discontinuous Galerkin spatial discretizations ⋮ Dahlquist's classical papers on stability theory ⋮ Note onA-stability of multistep multiderivative methods ⋮ A-stable linear multistep methods for Volterra integro-differential equations ⋮ Galerkin-Obrechkoff methods and hyperbolic initial boundary value problems with damping ⋮ Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Form \(u_{xy}=f(x,y,u,u_x,u_y)\) ⋮ Arithmetic tests forA-stability,A[α-stability, and stiff-stability] ⋮ Order stars and stability theorems ⋮ Stiffly stable second derivative multistep methods with higher order and improved stability regions

Cites Work

• Multistep-multistage-multiderivative methods for ordinary differential equations
• Finite Difference Forms Containing Derivatives of Higher Order
• A -Stable Composite Multistep Methods
• A special stability problem for linear multistep methods
• A New Class of Orthogonal Polynomials: The Bessel Polynomials
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