Derivation of Numerical Methods Using Computer Algebra

DOI10.1137/S003614459935093XzbMath0981.65003OpenAlexW1985953035MaRDI QIDQ4699115

Dominik Gruntz, Walter Gander

Publication date: 23 November 1999

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s003614459935093x

zbMATH Keywords

Galerkin methodfinite elementsquadrature formulasRunge-Kutta methodcomputer algebranonlinear equationsRayleigh-Ritz methodsecant methodMapleNewton's iterationGaussian integrationscientific computationtutorial paperNewton-Cotes integration

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to single equations (65H05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical quadrature and cubature formulas (65D32) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01) Mathematics teaching methods and classroom techniques (97D40)

Related Items (6)

Embedded explicit Runge-Kutta type methods for directly solving special third order differential equations \(y = f(x, y)\) ⋮ Two embedded pairs of Runge-Kutta type methods for direct solution of special fourth-order ordinary differential equations ⋮ Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations ⋮ Generating numerical algorithms using a computer algebra system ⋮ Solving oscillatory delay differential equations using block hybrid methods ⋮ Composite group of explicit Runge-Kutta methods

Uses Software

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