Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method

DOI10.3390/a9010018zbMath1461.65094OpenAlexW2294488377MaRDI QIDQ1736773

Uswah Qasim, Fayyaz Ahmad, Mir Asma, Zulifqar Ali, Malik Zaka Ullah, Stefano Serra Capizzano

Publication date: 26 March 2019

Published in: Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/a9010018

zbMATH Keywords

ordinary differential equationshomotopy methodsystems of nonlinear equationspartial differential equationsfrozen Jacobian

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)

Related Items (4)

Moving mesh strategies of adaptive methods for solving nonlinear partial differential equations ⋮ Multi-step preconditioned Newton methods for solving systems of nonlinear equations ⋮ Frozen Jacobian multistep iterative method for solving nonlinear IVPs and BVPs ⋮ An eighth order frozen Jacobian iterative method for solving nonlinear IVPs and BVPs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system
• On shifted Jacobi spectral method for high-order multi-point boundary value problems
• Modified homotopy perturbation technique for the approximate solution of nonlinear equations
• The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves
• Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
• Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs
• Iterative methods improving Newton's method by the decomposition method
• Generation of root finding algorithms via perturbation theory and some formulas
• An efficient multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with ODEs
• Two-parameter homotopy method for nonlinear equations
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method
• On the homotopy analysis method for nonlinear problems.
• Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs
• Newton-homotopy analysis method for nonlinear equations
• Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications
• Newton's method with deflation for isolated singularities of polynomial systems
• An Efficient Legendre Pseudospectral Method for Solving Nonlinear Quasi Bang-Bang Optimal Control Problems
• A Mesh-Independence Principle for Operator Equations and Their Discretizations
• Analytic solutions of the temperature distribution in Blasius viscous flow problems
• Some iterative methods for solving nonlinear equations using homotopy perturbation method

This page was built for publication: Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method