An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs

DOI10.1016/j.aml.2021.107767zbMath1485.65057OpenAlexW3208401886MaRDI QIDQ2060838

Wenrui Hao

Publication date: 13 December 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107767

zbMATH Keywords

nonlinear dynamicsnonlinear parametric systemsadaptive homotopy tracking

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Cites Work

• Unnamed Item
• Unnamed Item
• A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
• Continuation along bifurcation branches for a tumor model with a necrotic core
• A homotopy for solving general polynomial systems that respects m- homogeneous structures
• A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations
• A bootstrapping approach for computing multiple solutions of differential equations
• An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
• Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws
• The CFL Condition for Spectral Approximations to Hyperbolic Initial-Boundary Value Problems
• Large-Scale Machine Learning with Stochastic Gradient Descent
• Adaptive Multiprecision Path Tracking
• On convergence rates for the iteratively regularized Gauss-newton method
• Total variation diminishing Runge-Kutta schemes
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

This page was built for publication: An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs