Globally convergent homotopy methods: A tutorial

DOI10.1016/0096-3003(89)90129-XzbMath0689.65033OpenAlexW3030835366MaRDI QIDQ582009

Layne T. Watson

Publication date: 1989

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0096-3003(89)90129-x

zbMATH Keywords

inverse problemfinite elementscollocationpolynomial systemscantilever beamstwo-point boundary value problemshomotopy methodsflow algorithmsJacobian matrix algorithmsparallel computationalpath-following algorithmsshooting, finite differencessoftware package HOMPACKzero-finding, optimization

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items

On higher-order differentiation in nonlinear mechanics, Symmetric homotopy construction, Homotopies for solving polynomial systems within a bounded domain, The homotopy analysis method to solve the Burgers-Huxley equation, A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations, A wavelet multiscale-adaptive homotopy method for the inverse problem of nonlinear diffusion equation, Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation, A wavelet multiscale-homotopy method for the inverse problem of two-dimensional acoustic wave equation, A homotopy method for bioluminescence tomography, A homotopy method for nonlinear inverse problems, A study on the \(d\)-dimensional Schrödinger equation with a power-law nonlinearity, Nonlinear embeddings: applications to analysis, fractals and polynomial root finding, Solving the inverse problem of identifying an unknown source term in a parabolic equation, The renormalization method based on the Taylor expansion and applications for asymptotic analysis, Nonlinear vibration analysis of functionally graded flow pipelines under generalized boundary conditions based on homotopy analysis, Analytical solution for arbitrary large deflection of geometrically exact beams using the homotopy analysis method, Bounded homotopy path approach to the solution of linear complementarity problems, On the general boundary element method, AN ALGORITHM FOR FINDING ALL ZEROS OF VECTOR FUNCTIONS, Exploring collision-free path planning by using homotopy continuation methods, A TFC-based homotopy continuation algorithm with application to dynamics and control problems, Reconstruction of a permeability field with the wavelet multiscale-homotopy method for a nonlinear convection-diffusion equation, Solving the backward heat conduction problem by homotopy analysis method, A homotopy-projection method for the parameter estimation problems, Nonlinear reduction for solving deficient polynomial systems by continuation methods, Numerical solutions of highly oscillatory integrals, A wavelet multiscale-homotopy method for the parameter identification problem of partial differential equations, A series solution of the foam drainage equation, Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, A series solution of the nonlinear Volterra and Fredholm integro-differential equations, A weighted algorithm based on the homotopy analysis method: application to inverse heat conduction problems, An algorithm for finding all solutions of a nonlinear system, The homotopy method for identifying the radiative source term in the heat conduction problem, Symbolic homotopy construction, A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space, Application of weighted homotopy analysis method to solve an inverse source problem for wave equation, Convergent scattering series solution of the inhomogeneous Helmholtz equation via renormalization group and homotopy continuation approaches, Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order \(H^2/H^\infty\) modeling, estimation, and control, An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

Uses Software

• PITCON
• minpack
• HOMPACK

Cites Work

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