We extend a collocation method for solving a nonlinear ordinary differential equation ODE via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in chemistry, physics, and so forth, see the works of Doha and Bhrawy 2006, Guo 2000, and Guo et al. 2002 . Choosing the optimal polynomial for solving every ODEs problem depends on many f...

In this work, Laplace transform-Legendre-wavelet collocation method is adopted for a semi-numerical analysis of predicting transient nonlinear behaviour radiative-convective fin with temperature-variant internal heat generation. The verification the results hybrid shown good agreements direct numerical and approximate analytical s in previous works. Parametric depicts significance model paramet...

The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

The development and production of high performance equipment necessitate the use of passive cooling technology. In this paper, heat transfer study of convective-radiative straight fin with temperature-dependent thermal conductivity under the influence of magnetic field is carried out using Legendre wavelet collocation method. The numerical solution is used to investigate the effects of magnetic...

A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...

In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Di...

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

in this paper, a new method is investigated for model order reduction of high order systems based on moment matching technique. in this method, at first, full order model is expanded by legendre wavelet function which is included in orthogonal functions. a suitable fixed structure model is considered as reduced order model whose parameters are unknown. these unknown parameters are determined us...

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multiorder fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is ve...