A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations

DOI10.1080/0020716031000079572zbMath1040.65061OpenAlexW2114004795MaRDI QIDQ4454323

Unnamed Author

Publication date: 8 March 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0020716031000079572

zbMATH Keywords

numerical examplespredictor-corrector methodinitial value problemscollocationlinear multistep method\(P\)-stability

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (26)

Boundary value technique based on a fifth derivative method of order 10 for fourth order initial and boundary value problems ⋮ Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method ⋮ A symmetric \(k\)-step method for direct integration of second order initial value problems of ordinary differential equations ⋮ Two embedded pairs of Runge-Kutta type methods for direct solution of special fourth-order ordinary differential equations ⋮ A sixth‐order improved <scp>Runge–Kutta</scp> direct method for special third‐order ordinary differential equations ⋮ Solving higher order nonlinear ordinary differential equations with least squares support vector machines ⋮ Hybrid methods for direct integration of special third order ordinary differential equations ⋮ \(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations ⋮ Fourth-order improved Runge-Kutta method for directly solving special third-order ordinary differential equations ⋮ Unnamed Item ⋮ Direct integrators of Runge-Kutta type for special third-order ordinary differential equations ⋮ The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations ⋮ A novel fixed point iteration method for the solution of third order boundary value problems ⋮ An efficient zero-stable numerical method for fourth-order differential equations ⋮ A functionally-fitted block Numerov method for solving second-order initial-value problems with oscillatory solutions ⋮ Algorithmic collocation approach for direct solution of fourth-order initial-value problems of ordinary differential equations ⋮ Direct integration of the third-order two point and multipoint Robin type boundary value problems ⋮ A direct variable step block multistep method for solving general third-order ODEs ⋮ New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method ⋮ Unnamed Item ⋮ Direct integrators for the general third-order ordinary differential equations with an application to the Korteweg-de Vries equation ⋮ A new integrator for special third order differential equations with application to thin film flow problem ⋮ A two-step hybrid block method with fourth derivatives for solving third-order boundary value problems ⋮ Explicit integrator of Runge-Kutta type for direct solution of \(u^{(4)} = f(x, u, u', u)\) ⋮ An accurate block hybrid collocation method for third order ordinary differential equations ⋮ A model for solving first, second and third order IVPs directly

Cites Work

• Unnamed Item
• Unnamed Item
• One-step multiderivative methods for first order ordinary differential equations
• A new sixth-order algorithm for general second order ordinary differential equations
• Mesh Selection in Collocation for Boundary Value Problems
• Multiderivative Methods for Periodic Initial Value Problems
• Order stars and stability theorems
• Numerical solution of high order boundary value problems for ordinary differential equations with an estimation of the error
• Some Characteristics of Implicit Multistep Multi-Derivative Integration Formulas
• A class of continuous methods for general second order initial value problems in ordinary differential equations
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

This page was built for publication: A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations