Conference Paper
Year 2013,
Volume: 26 Issue: 4, 527 - 534, 02.01.2014
Abstract
References
- Farouki, R.T. and Rajan, V.T., Algorithms for polynomials in Bernstein form, Computer Aided Geometric Design, 5: 1-26, (1988).
- Farin, G., Curves and surfaces for CAGD fifth edition, Academic Press, United States of America, (2002).
- Bhatti, M.I. and Bracken, P., Solutions of differential equations in a Bernstein polynomial basis, Journal of Computational and Applied Mathematics, 205: 272-280, (2007).
- Doha, E.H., Bhrawy, A.H. and Saker, M.A., On the derivatives of Bernstein polynomials: An application for the solution of high even-order differential equations, Boundary Value Problems, 2011: 1-16, (2011).
- Doha, E. H., Bhrawy, A. H. and Saker, M. A., Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations, Applied Mathematics Letters, 24: 559- 565, (2011).
- Işık, O.R., Sezer, M. and Güney, Z., A Rational approximation based on Bernstein polynomials for high order initial and boundary value problems, Applied Mathematics and Computation, 217: 9438-9450, (2011).
- Işık, O.R., Güney, Z. and Sezer, M., Bernstein series solutions of pantograph equations using polynomial interpolation, Journal of Difference Equations and Applications, 18: 357-374, (2010).
- Ordokhani, Y. and Davaei far, S., Approximate solutions of differential equations by using the Bernstein polynomials, International Scholarly Research Network ISRN Applied Mathematics, 2011: 1-15, (2011).
- Bhattacharya, S. and Mandal, B.N., Use of Bernstein polynomials in numerical solutions of Volterra integral equations, Applied Mathematical Sciences, 2: 1773-1787, (2008).
- Shirin, A. and Islam, A.S., Numerical solutions of Fredholm integral equations using Bernstein polynomials, Journal of Scientific Research, 2: 264-272, (2010).
- Bhatta, D.D. and Bhatti, M.I, Numerical Solution of KdV equation using modified Bernstein polynomials, Computation, 174: 1255-1268, (2006). Mathematics and
- Stewart, G.W., Matrix algorithms volume I: Basic decompositions, SIAM, Philadelphia, (1998).
- Yousefi, S.A. and Dehghan, B.M., Bernstein Ritz- Galerkin method for solving an initial-boundary value problem that combines Neumann and integral condition for the wave equation, Numerical Methods for Partial Differential Equations, 26: 1236-1246, (2009).
- Bhattacharya, S. and Mandal, B.N., Numerical solution of a singular integro- differential equation, Applied Mathematics and Computation, 195: 346- 350, (2008).
- Lorentz, G.G., Bernstein polynomials, Chelsea Publishing, New York, N.Y., (1986).
- Rivlin, T.J., An introduction to the approximation of functions, Dover Publications, N.Y., (2003).
- Siddiqi, S.S. and Akram, G., Septic spline solutions of sixth-order boundary value problems, Journal Mathematics, 215: 288-301, (2008). and Applied
- El-Gamel, M., Cannon, J.R. and Zayed, A.I., Sinc- Galerkin method for solving linear sixth-order boundary value problems, Mathematics and Computation, 73: 1325-1343, (2003).
Year 2013,
Volume: 26 Issue: 4, 527 - 534, 02.01.2014
Abstract
In this study, a new collocation method based on Bernstein polynomials defined on the interval [a, b] is introduced for approximate solutions of initial and boundary value problems involving higher order linear differential equations with variable coefficients. Error analysis of the method is demonstrated. Some numerical solutions are given to illustrate the accuracy, efficiency and implementation of the method, and the results of the proposed method are also compared with the other methods in several examples.
References
- Farouki, R.T. and Rajan, V.T., Algorithms for polynomials in Bernstein form, Computer Aided Geometric Design, 5: 1-26, (1988).
- Farin, G., Curves and surfaces for CAGD fifth edition, Academic Press, United States of America, (2002).
- Bhatti, M.I. and Bracken, P., Solutions of differential equations in a Bernstein polynomial basis, Journal of Computational and Applied Mathematics, 205: 272-280, (2007).
- Doha, E.H., Bhrawy, A.H. and Saker, M.A., On the derivatives of Bernstein polynomials: An application for the solution of high even-order differential equations, Boundary Value Problems, 2011: 1-16, (2011).
- Doha, E. H., Bhrawy, A. H. and Saker, M. A., Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations, Applied Mathematics Letters, 24: 559- 565, (2011).
- Işık, O.R., Sezer, M. and Güney, Z., A Rational approximation based on Bernstein polynomials for high order initial and boundary value problems, Applied Mathematics and Computation, 217: 9438-9450, (2011).
- Işık, O.R., Güney, Z. and Sezer, M., Bernstein series solutions of pantograph equations using polynomial interpolation, Journal of Difference Equations and Applications, 18: 357-374, (2010).
- Ordokhani, Y. and Davaei far, S., Approximate solutions of differential equations by using the Bernstein polynomials, International Scholarly Research Network ISRN Applied Mathematics, 2011: 1-15, (2011).
- Bhattacharya, S. and Mandal, B.N., Use of Bernstein polynomials in numerical solutions of Volterra integral equations, Applied Mathematical Sciences, 2: 1773-1787, (2008).
- Shirin, A. and Islam, A.S., Numerical solutions of Fredholm integral equations using Bernstein polynomials, Journal of Scientific Research, 2: 264-272, (2010).
- Bhatta, D.D. and Bhatti, M.I, Numerical Solution of KdV equation using modified Bernstein polynomials, Computation, 174: 1255-1268, (2006). Mathematics and
- Stewart, G.W., Matrix algorithms volume I: Basic decompositions, SIAM, Philadelphia, (1998).
- Yousefi, S.A. and Dehghan, B.M., Bernstein Ritz- Galerkin method for solving an initial-boundary value problem that combines Neumann and integral condition for the wave equation, Numerical Methods for Partial Differential Equations, 26: 1236-1246, (2009).
- Bhattacharya, S. and Mandal, B.N., Numerical solution of a singular integro- differential equation, Applied Mathematics and Computation, 195: 346- 350, (2008).
- Lorentz, G.G., Bernstein polynomials, Chelsea Publishing, New York, N.Y., (1986).
- Rivlin, T.J., An introduction to the approximation of functions, Dover Publications, N.Y., (2003).
- Siddiqi, S.S. and Akram, G., Septic spline solutions of sixth-order boundary value problems, Journal Mathematics, 215: 288-301, (2008). and Applied
- El-Gamel, M., Cannon, J.R. and Zayed, A.I., Sinc- Galerkin method for solving linear sixth-order boundary value problems, Mathematics and Computation, 73: 1325-1343, (2003).
There are 18 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | January 2, 2014 |
| Published in Issue | Year 2013 Volume: 26 Issue: 4 |