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Home  >  Volume 43

10. Numerical Solution of Nonlinear Singular Ordinary Differential Equations Arising in Biology via Operational Matrix of Bernstein Polynomials by Olagunju Adeyemi S.JNAMP Volume 43,(Sept. and Nov., 2017), 61 – 66
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In this paper, a numerical method based on Bernstein polynomial defined on the interval [0 1] is applied for the solution of nonlinear singular differential equation that arises in modelling of some diseases and biology. These nonlinear problems are solved by first writing the solution as a linear combination of Bernstein basis functions. Established properties of Bernstein polynomials together with operation matrix of its derivatives are employed to express each term in the given equation in easy-to-handle form, such that the problem of finding solution of nonlinear differential equations is reduced to problems of finding solution to algebraic equations which are easily handled by an algebraic solver- MATLAB. The method is computationally efficient and applications are demonstrated via some numerical examples.

Keywords: Nonlinear Singular Boundary Value Problem; Bernstein polynomials; Physiology; Biology