IEEE

Solving Nonlinear Multi-Order Fractional Differential Equations Using Bernstein Polynomials

Abstract: This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational ...
Scientific Research Publishing

Numerical Solution of Integro-Differential Equations with Local Polynomial Regression ()

Library, Chongqing University of Technology, Chongqing, China. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China. [1] B. Asady and M. T. Kajani, “Direct Method ...
IEEE

On the Numerical Approximation of First-order Riccati Differential Equations by Two-step Second Derivative Block Method with Bernstein Polynomial Basis

Abstract: A new two-step second derivative block method (TSDBM) using Bernstein polynomial of convergence order six for solving Riccati Differential Equations (RDEs) is presented. The TSDBM is ...
JSTOR Daily

A Polynomial Representation of Hybrid Methods for Solving Ordinary Differential Equations

Mathematics of Computation, Vol. 33, No. 148 (Oct., 1979), pp. 1251-1256 (6 pages) A polynomial representation of the hybrid methods for solving ordinary differential equations is presented. The ...
JSTOR Daily

Appell Polynomials and Differential Equations of Infinite Order

Let Φ(z) = ∑∞ 0 βjz j have radius of convergence $r (0 < r < \infty)$ and no singularities other than poles on the circle |z| = r. A complete solution is ...
Europe PMC

Neural minimization methods (NMM) for solving variable order fractional delay differential equations (FDDEs) with simulated annealing (SA).

To enrich any model and its dynamics introduction of delay is useful, that models a precise description of real-life phenomena. Differential equations in which current time derivatives count on the ...
Scientific Research Publishing

Mahmoudi, Y., Abdollahi, M., Karimian, N. and Khalili, H. (2012) Adomian Decomposition Method with Laguerre Polynomials for Solving Ordinary Differential Equation. Journal of ...

ABSTRACT: The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations ...