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| Content Provider | Springer Nature Link |
|---|---|
| Author | Behroozifar, Mahmoud |
| Copyright Year | 2015 |
| Abstract | A spectral method based on operational matrices of Bernstein polynomials using collocation method is elaborated and employed for solving nonlinear ordinary and partial differential equations with multi-point boundary conditions. First, properties of Bernstein polynomial, operational matrices of integration, differentiation and product are introduced and then utilized to reduce the given differential equation to the solution of a system of algebraic equations. This new approach provides a significant computational advantage by converting the given original problem to an equivalent integro-differential equation which implies all boundary condition. Approximate solution is achieved by expanding the desired function in terms of a Bernstein basis and employing operational matrices. Unknown coefficients are determined by collocation. The method is compared with modified Adomian decomposition method, Birkhoff-type interpolation method, reproducing kernel Hilbert space method, fixed point method, finite-difference Keller-box method, multilevel augmentation method and shooting method. Illustrative examples are included to demonstrate the high precision, validity and good performance of the new scheme even for solving nonlinear singular differential equations. |
| Ending Page | 925 |
| Page Count | 25 |
| Starting Page | 901 |
| File Format | |
| ISSN | 00063835 |
| e-ISSN | 15729125 |
| Journal | BIT Numerical Mathematics |
| Issue Number | 4 |
| Volume Number | 55 |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2015-01-21 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Computational Mathematics and Numerical Analysis Nonlinear differential equations Numeric Computing Mathematics Initial value problems for nonlinear higher-order equations Spectral methods Bernstein basis Spectral, collocation and related methods Collocation spectral method Operational matrix Nonlinear boundary value problems Numerical approximation of solutions Multi-point boundary value problem |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Computer Networks and Communications Computational Mathematics Software |
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