A Taylor series method for the numerical solution of two-point boundary value problems

DOI10.1007/BF01404566zbMath0421.65051OpenAlexW2088137141MaRDI QIDQ1133304

Peter Rentrop

Publication date: 1979

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132585

zbMATH Keywords

algorithmrecurrence formulassuperconductivityTaylor series methodshooting algorithmnonlinear shell theorychemistry

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Shells (74K25) Electromagnetic theory (general) (78A25) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Dynamical problems in solid mechanics (74H99)

Related Items (14)

Solving nonlinear reaction-diffusion problem in electrostatic interaction with reaction-generated ph change on the kinetics of immobilized enzyme systems using Taylor series method ⋮ Methods for solving singular boundary value problems using splines: a review ⋮ Cubic spline polynomial for non-linear singular two-point boundary value problems ⋮ Single step methods for general second order singular initial value problems with spherical symmetry ⋮ A stepsize control for continuation methods and its special application to multiple shooting techniques ⋮ Singular boundary value problems for ODEs ⋮ Status of the differential transformation method ⋮ Secant methods for sparse systems of nonlinear equations with a special structure ⋮ Efficient shooting method for solving two point boundary value problems ⋮ Bibliography on the evaluation of numerical software ⋮ Changing variables in Taylor series with applications to PDEs ⋮ Convergence analysis and detection of singularities within a boundary meshless method based on Taylor series ⋮ Stability curves for thin spherical caps and hemispheres ⋮ Least‐square collocation and Lagrange multipliers forTaylor meshless method

Cites Work

• A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
• Implicit Runge-Kutta methods for second kind Volterra integral equations
• Numerical solution of the singular Ginzburg-Landau equations by multiple shooting
• Comparing routines for the numerical solution of initial value problems of ordinary differential equations in multiple shooting
• Numerical treatment of ordinary differential equations by extrapolation methods
• Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• On the Nonlinear Theory of Shallow Spherical Shells
• A Program for the Automatic Integration of Differential Equations using the Method of Taylor Series
• Quasi-Newton Methods and their Application to Function Minimisation
• On Finite Symmetrical Deflections of Thin Shells of Revolution
• Axisymmetric buckling of hollow spheres and hemispheres
• The automatic solution of systems of ordinary differential equations by the method of Taylor series
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