529 research outputs found
Homotopy perturbation method to space–time fractional solidification in a finite slab
AbstractA mathematical model describing the space and time fractional solidification of fluid initially at its freezing temperature contained in a finite slab under the constant wall temperature is presented. The approximate analytical solution of this problem is obtained by the homotopy perturbation method. The results thus obtained are compared with exact solution of integer order (β=1,α=2) and are good agreement. The problem has been studied in detail by considering different order time and space fractional derivatives. The temperature distribution and the moving interface position for different fractional order space and time derivatives are shown graphically. The model and the solution are the generalization of the previous works and include them as special cases
A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
In this paper, the fractional order of rational Bessel functions collocation
method (FRBC) to solve Thomas-Fermi equation which is defined in the
semi-infinite domain and has singularity at and its boundary condition
occurs at infinity, have been introduced. We solve the problem on semi-infinite
domain without any domain truncation or transformation of the domain of the
problem to a finite domain. This approach at first, obtains a sequence of
linear differential equations by using the quasilinearization method (QLM),
then at each iteration solves it by FRBC method. To illustrate the reliability
of this work, we compare the numerical results of the present method with some
well-known results in other to show that the new method is accurate, efficient
and applicable
Numerical investigation of Differential Biological-Models via GA-Kansa Method Inclusive Genetic Strategy
In this paper, we use Kansa method for solving the system of differential
equations in the area of biology. One of the challenges in Kansa method is
picking out an optimum value for Shape parameter in Radial Basis Function to
achieve the best result of the method because there are not any available
analytical approaches for obtaining optimum Shape parameter. For this reason,
we design a genetic algorithm to detect a close optimum Shape parameter. The
experimental results show that this strategy is efficient in the systems of
differential models in biology such as HIV and Influenza. Furthermore, we prove
that using Pseudo-Combination formula for crossover in genetic strategy leads
to convergence in the nearly best selection of Shape parameter.Comment: 42 figures, 23 page
A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation
A fractional Stefan problem with a boundary convective condition is solved,
where the fractional derivative of order is taken in the
Caputo sense. Then an equivalence with other two fractional Stefan problems
(the first one with a constant condition on and the second with a
flux condition)is proved and the convergence to the classical solutions is
analyzed when recovering the heat equation with its
respective Stefan condition.Comment: This paper was already accepted to be published in the in the journal
"Fractional Calculus and Applied Analysis". arXiv admin note: substantial
text overlap with arXiv:1306.175
A semi analytic iterative method for solving two forms of blasius equation / Mat Salim Selamat, Nurul Atkah Halmi and Nur Azyyati Ayob
In this paper, a semi analytic iterative method (SAIM) is presented for solving two forms of Blasius equation. Blasius equation is a third order nonlinear ordinary differential equation in the problem of the two-dimensional laminar viscous flow over half-infinite domain. In this scheme, the first solution which is in a form of convergent series solution is combined with Padé approximants to handle the boundary condition at infinity. Comparison the results obtained by SAIM with those obtained by other method such as variational iteration method and differential transform method revealed the effectiveness of the SAIM
- …