23 research outputs found
Analytic Solutions of Some Self-Adjoint Equations by Using Variable Change Method and Its Applications
No full textMany applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011; Borhanifar et al. 2011; Sweilam and Nagy, 2011; Gülsu et al. 2011; Mohyud-Din et al. 2010; and Li et al. 1996)
An Accurate Numerical Method for Solving Unsteady Isothermal Flow of a Gas Through a Semi-Infinite Porous Medium
No full textThe Kidder equation, y″(x)+2xy′(x)/1−βy(x)=0, x∈[0,∞), β∈[0,1] with y(0)=1, and y(∞)=0, is a second-order nonlinear two-point boundary value ordinary differential equation (ODE) on the semi-infinite domain, with a boundary condition in the infinite that describes the unsteady isothermal flow of a gas through a semi-infinite micro–nano porous medium and has widely used in the chemical industries. In this paper, a hybrid numerical method is introduced for solving this equation. First, by using the method of quasi-linearization, the equation is converted to a sequence of linear ODEs. Then these linear ODEs are solved by using the rational Legendre functions (RLFs) collocation method. By using 200 collocation points, we obtain a very good approximation solution and the value of the initial slope y′(0)=−1.19179064971942173412282860380015936403 for β=0.50, highly accurate to 38 decimal places. The convergence of numerical results is shown by decreasing the residual errors when the number of collocation points increases.</jats:p
The generalized fractional order of the Chebyshev functions on nonlinear boundary value problems in the semi-infinite domain
No full textAbstractA new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.</jats:p
Generalized Lagrange Jacobi‐Gauss‐Lobatto vs Jacobi‐Gauss‐Lobatto collocation approximations for solving (2 + 1)‐dimensional Sine‐Gordon equations
No full textOperational matrices to solve nonlinear Riccati differential equations of arbitrary order
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Systems of nonlinear Volterra integro-differential equations of arbitrary order
No full textIn this paper, a new approximate method for solving of systems of nonlinear Volterra integro-differential equations of arbitrary (integer and fractional) order is introduced. For this purpose, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) based on the classical Chebyshev polynomials of the first kind has been introduced that can be used to obtain the solution of the integro-differential equations (IDEs). Also, we construct the fractional derivative operational matrix of order in the Caputo's definition for GFCFs. This method reduced a system of IDEs by collocation method into a system of algebraic equations. Some examples to illustrate the simplicity and the effectiveness of the propose method have been presented.</jats:p
Solving the Boundary Layer Flow of Eyring–Powell Fluid Problem via Quasilinearization–Collocation Method Based on Hermite Functions
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