[PDF] Top 20 Numerical Study of Fractional Differential Equations of Lane Emden Type by Method of Collocation

... of fractional differential equations of various types plays important roles and tools not only in ma- thematics but also in physics, control systems, dynamical systems and engineering to create the ... See full document

... we study the fractional order Lane-Emden differential equations by using the reproducing kernel ...Some numerical examples are given in order to demonstrate the accuracy of the ... See full document

... sinc-collocation method is used to approximate the solution of multi-order fractional differential equations with initial ...This method converts the FDEs into a system of ... See full document

... This method constructs a semi-analytical numerical technique that uses Taylor series for the solution of differential equations in the form of ...series method which requires symbolic ... See full document

... this study, the several Lane-Emden type equations will be ...These equations will be tested by the above- mentioned algorithms, which will ultimately show the usefulness and ... See full document

... to numerical solutions for other values of k but the singularity at x = 0 is still a challenge to the numerical ...Decomposition Method (ADM) and perturba- tion techniques and mostly convergent in ... See full document

... a numerical method based on the Bessel poly- nomials and collocation points for solving the Lane-Emden equations ...and collocation points, this method transforms ... See full document

... by fractional differential equa- tions and hence the study of these type of equations is very important due to their frequent appearance in various appli- cations in fluid mechanics, ... See full document

... failed, fractional calculus is getting enormous attention ...for numerical approximations of various types of fractional differential ...For fractional diffusion equations ... See full document

... differential equations of Lane-Emden type are solved using the boundary value ...multistep collocation technique. The tech- nique transforms the numerical methods to a system of ... See full document

... Many numerical methods were developed for this type of nonlinear ordinary differential equations, specifi- cally on Lane-Emden type equations such as the Adomian ... See full document

... the study of singular initial value problems modelled by second order nonlinear ordinary differential equations[1, 2] has attracted many mathematicians and ...important equations in this literature is ... See full document

... differential equations are considered. From the numerical result, we can find that the Adomian decomposition method is an efficient ...the numerical result has high precision. In ... See full document

... expansion method, based on orthonormal polyno- mials to solve ...presented method on three test problems and showed that the numerical results have high accuracy comparing with exact val- ... See full document

... A numerical method based on B-spline is developed to solve the time-dependent Emden-Fow- ler-type ...the method is described. Numerical results are given to illustrate the ... See full document

... [3], collocation [11], finite differ- ence method [7], Galerkin [40], He’s variational iteration [15, 24, 27], homotopy analysis [12], homotopy perturbation [25], Laplace transform [10], reproducing kernel ... See full document

... Fuzzy Fractional Initial Value Problem under Caputo- type fuzzy fractional derivatives by a modified fractional Euler ...merical method for solving FFDE is an area not yet widely ... See full document

... block method to have the most accurate solution for Jerk Equation ...the method derivation, Section 3 presents the analysis of the method involving order four, Section 4 presents the numerical ... See full document

... integro-differential equations in Lebesgue spaces are stud- ...integro-differential equations discussed in this ...Direct numerical schemes using a collocation method and ... See full document

... the numerical point of view, such as the Legendre wavelet method, the spectral method and quartered shifted Legendre method based on Gauss ...Euler’s method has been proven to be ... See full document