On the solution of the polynomial systems arising in the discretization of certain ODEs

DOI10.1007/s00607-009-0046-7zbMath1173.65035OpenAlexW2112734325MaRDI QIDQ836949

Guillermo Matera, Ezequiel Dratman

Publication date: 9 September 2009

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-009-0046-7

zbMATH Keywords

complexityalgorithmconvergencepositive solutionscondition numbersemilinear heat equationinitial-value problemstationary solutionssemi-discretizationfinite-differenceshomotopy continuation methodtwo-point boundary-value problemnonlinear Neumann boundary condition

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear parabolic equations (35K55) Nonlinear boundary value problems for ordinary differential equations (34B15) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Complexity and performance of numerical algorithms (65Y20) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (5)

Approximation of the solution of certain nonlinear ODEs with linear complexity ⋮ Complexity of certain nonlinear two-point BVPs with Neumann boundary conditions ⋮ Efficient approximation of the solution of certain nonlinear reaction-diffusion equations with small absorption ⋮ Exploring collision-free path planning by using homotopy continuation methods ⋮ Newton's method and a mesh-independence principle for certain semilinear boundary-value problems

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