Bernstein polynomial basis for numerical solution of boundary value problems

DOI10.1007/s11075-017-0311-3zbMath1381.65058OpenAlexW2598137088MaRDI QIDQ679710

Khadigeh Shabanpanah, Hamid Reza Tabrizidooz

Publication date: 19 January 2018

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0311-3

zbMATH Keywords

numerical examplesecond-order differential equationsnonlinearlineartwo-point boundary value problemsapproximation erroroperational matricesBernstein polynomial basis

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (3)

An efficient numerical technique for solving nonlinear singularly perturbed reaction diffusion problem ⋮ An efficient technique based on Green's function for solving two-point boundary value problems and its convergence analysis ⋮ A numerical comparative study of generalized Bernstein-Kantorovich operators

Uses Software

• Chebfun

Cites Work

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• A new spectral method for a class of linear boundary value problems
• An analytical approach for solving nonlinear boundary value problems in finite domains
• Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations
• The dual basis functions for the Bernstein polynomials
• Shifted Legendre direct method for variational problems
• A Walsh series direct method for solving variational problems
• Efficient collocation schemes for singular boundary value problems
• Approximate solution of linear ordinary differential equations with variable coefficients
• Solutions of differential equations in a Bernstein polynomial basis
• Computing numerically with functions instead of numbers
• Operational matrices of Bernstein polynomials and their applications
• Shifted Chebyshev direct method for solving variational problems
• Shooting methods for the Schrodinger equation
• Fourier series direct method for variational problems
• Sine-cosine wavelets operational matrix of integration and its applications in the calculus of variations
• The Haar wavelets operational matrix of integration
• Orthogonal polynomial solutions of linear ordinary differential equations

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