77 research outputs found
An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method
Based on a new approximation method, namely pseudospectral method, a solution
for the three order nonlinear ordinary differential laminar boundary layer
Falkner-Skan equation has been obtained on the semi-infinite domain. The
proposed approach is equipped by the orthogonal Hermite functions that have
perfect properties to achieve this goal. This method solves the problem on the
semi-infinite domain without truncating it to a finite domain and transforming
domain of the problem to a finite domain. In addition, this method reduces
solution of the problem to solution of a system of algebraic equations. We also
present the comparison of this work with numerical results and show that the
present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of
"Communications in Nonlinear Science and Numerical Simulation
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
Numerical approximations for population growth model by Rational Chebyshev and Hermite Functions collocation approach: A comparison
This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF)
collocation approach to solve the Volterra's model for population growth of a
species within a closed system. This model is a nonlinear integro-differential
equation where the integral term represents the effect of toxin. This approach
is based on orthogonal functions which will be defined. The collocation method
reduces the solution of this problem to the solution of a system of algebraic
equations. We also compare these methods with some other numerical results and
show that the present approach is applicable for solving nonlinear
integro-differential equations.Comment: 18 pages, 5 figures; Published online in the journal of "Mathematical
Methods in the Applied Sciences
Improved Laguerre Spectral Methods with Less Round-off Errors and Better Stability
Laguerre polynomials are orthogonal polynomials defined on positive half line
with respect to weight . They have wide applications in scientific and
engineering computations. However, the exponential growth of Laguerre
polynomials of high degree makes it hard to apply them to complicated systems
that need to use large numbers of Laguerre bases. In this paper, we introduce
modified three-term recurrence formula to reduce the round-off error and to
avoid overflow and underflow issues in generating generalized Laguerre
polynomials and Laguerre functions. We apply the improved Laguerre methods to
solve an elliptic equation defined on the half line. More than one thousand
Laguerre bases are used in this application and meanwhile accuracy close to
machine precision is achieved. The optimal scaling factor of Laguerre methods
are studied and found to be independent of number of quadrature points in two
cases that Laguerre methods have better convergence speeds than mapped Jacobi
methods.Comment: 19pages, 8 figure
Mixed Pseudospectral Method for Heat Transfer
In this paper, we propose a mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer with inhomogeneous boundary conditions on an infinite strip. Some properties about the mixed generalized LaguerreLegendre approximation are established. By reformulating the equation with suitable functional transform defined on an infinite strip, a mixed Laguerre-Legendre pseudospectral scheme is constructed. Its convergence is proved. Numerical results are presented to demonstrate the efficiency of this new approach and to validate our theoretical analysis
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