in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

The three-dimensional high-order simulation algorithm HOSIM is developed to simulate complex nonlinear and non-Gaussian systems. HOSIM is an alternative to the current MP approaches and it is based upon new high-order spatial connectivity measures, termed high-order spatial cumulants. The HOSIM algorithm implements a sequential simulation process, where local conditional distributions are gener...

This paper proposes and investigates a method for reducing potential numerical instability in the fast spherical harmonic transform algorithms proposed previously in [5,11]. The key objective of this study is a numerically reliable fast algorithm for computing the discrete Legendre transform (DLT); that is, the projection of sampled data onto the associated Legendre functions within a specified...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ball...