Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function
DOI10.2298/FIL1804379BzbMath1499.49082MaRDI QIDQ5023809
Publication date: 24 January 2022
Published in: Filomat (Search for Journal in Brave)
Bernstein polynomialscalculus of variationsvariational problemsEuler-Lagrange equationoperational matrix of differentiation
Existence theories for free problems in two or more independent variables (49J10) Polynomials in number theory (11C08) Numerical methods for initial value problems involving ordinary differential equations (65L05) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by operators (in particular, by integral operators) (41A35) Basic linear algebra (15A99) Discrete approximations in optimal control (49M25) Matrices, determinants in number theory (11C20) Existence theories for optimal control problems involving relations other than differential equations (49J21)
Related Items (3)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bernstein series solution of a class of Lane-Emden type equations
- A rational approximation based on Bernstein polynomials for high order initial and boundary values problems
- Solution of problems in calculus of variations via He's variational iteration method
- The use of Adomian decomposition method for solving problems in calculus of variations
- An efficient algorithm for solving multi-pantograph equation systems
- Direct Walsh-wavelet packet method for variational problems
- Bernstein series solution of a class of linear integro-differential equations with weakly singular kernel
- Collocation and residual correction
- Shifted Legendre direct method for variational problems
- Laguerre series direct method for variational problems
- A Walsh series direct method for solving variational problems
- Bernstein collocation method for solving nonlinear differential equations
- On Bernstein polynomials method to the system of Abel integral equations
- The numerical solution of problems in calculus of variation using B-spline collocation method
- Bernstein operational matrix with error analysis for solving high order delay differential equations
- Formulation of Euler-Lagrange equations for fractional variational problems
- Bernstein operational matrix of fractional derivatives and its applications
- Solutions of differential equations in a Bernstein polynomial basis
- Approximate solutions of singular two-point BVPs using Legendre operational matrix of differentiation
- A numerical method for solving some model problems arising in science and convergence analysis based on residual function
- Collocation method and residual correction using Chebyshev series
- Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the tau method with an error estimation
- Bernstein series solutions of pantograph equations using polynomial interpolation
- A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems
- Operational matrices of Bernstein polynomials and their applications
- Solving variational problems by homotopy–perturbation method
- Shifted Chebyshev direct method for solving variational problems
- Fourier series direct method for variational problems
- Classes of high-order numerical methods for solution of certain problem in calculus of variations
- Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations
- Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials
This page was built for publication: Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function
