Bernstein polynomials for solving fractional heat- and wave-like equations

“…Maleknejad et al [32] proposed a Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations. Rostamy and Karimi [33] solved fractional heat-and wave-like equations using Bernstein polynomials. Some numerical integration methods based on Bernstein polynomials are introduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

A numerical study for off-centered stagnation flow towards a rotating disc

Heydari

Loghmani

Rashidi

et al. 2015

Propulsion and Power Research

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In this investigation, a semi-numerical method based on Bernstein polynomials for solving off-centered stagnation flow towards a rotating disc is introduced. This method expands the desired solutions in terms of a set of Bernstein polynomials over a closed interval and then makes use of the tau method to determine the expansion coefficients to construct approximate solutions. This method can satisfy boundary conditions at infinity. The properties of Bernstein polynomials are presented and are utilized to reduce the solution of governing nonlinear equations and their associated boundary conditions to the solution of algebraic equations. Graphical results are presented to investigate the influence of the rotation ratio α on the radial velocity, azimuthal velocity and the induced velocities. A comparative study with the previous results of viscous fluid flow in the literature is made.

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“…Maleknejad et al (2012Maleknejad et al ( , 2011 proposed a Computational method based on Bernstein operational matrices for nonlinear Volterra-Fredholm-Hammerstein integral equations. Rostamy and Karimi (2012) solved fractional heat-and wave-like equations using Bernstein polynomials.…”

Section: Introductionmentioning

confidence: 99%

Exponential Bernstein functions: an effective tool for the solution of heat transfer of a micropolar fluid through a porous medium with radiation

2015

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In this study, an effective collocation method using new weighted orthogonal basis functions on the half-line, namely the exponential Bernstein functions, is proposed for simulating the solution of the heat transfer of a micropolar fluid through a porous medium with radiation. The governing equations and their associated boundary conditions can be written as a system of nonlinear ordinary differential equations. The presented approach does not require truncating or transforming the semi-infinite domain of the problem to a finite domain. In addition, this method reduces the solution of the problem to the solution of a system of algebraic equations. The effects of the coupling constant, radiation parameter and the permeability parameter on velocity and temperature profiles will be discussed in detail and shown graphically. A comparative study with the previous results of viscous fluid in the literature is made.

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Bernstein polynomials for solving fractional heat- and wave-like equations

Cited by 29 publications

References 18 publications

The Analytical Solution Of Singularly Perturbed Boundary Value Problems

The Analytical Solution Of Singularly Perturbed Boundary Value Problems

A numerical study for off-centered stagnation flow towards a rotating disc

Exponential Bernstein functions: an effective tool for the solution of heat transfer of a micropolar fluid through a porous medium with radiation

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