Analytical Solution of Multi-Pantograph Delay Differential Equations Via Sumudu Decomposition Method

In this paper, we apply Sumudu Decomposition Method (SDM) to solve the multi-pantograph delay differential equations with constant coefficients. Three problems are resolved to show the effectiveness and consistency of the SDM. The obtained results by this method provide solutions in a series form and in few terms. This technique successfully determines the convergence of the solution. Keywords: Sumudu Decomposition Method (SDM), Multi-Pantograph Delay Differential Equation

An Efficient Sumudu Decomposition Method to Solve System of Pantograph Equations

This paper is the witness of the coupling of decomposition method with the efficient Sumudu transform known as Sumudu decomposition method to build up the exact solutions of the linear and nonlinear system of Pantograph model equations. Three mathematical models are tested to elucidate effectiveness of the method. The obtained numerical results re-confirm the potential of the proposed method. In nonlinear cases this method uses He’s Polynomials for solving the non-linear terms. It is observed that suggested scheme is highly reliable and may be extended to other highly nonlinear delay differential models. Keywords: Decomposition method, Sumudu transform, System of multi-Pantograph delay differential equations, He’s polynomial

Stability of numerical method for semi-linear stochastic pantograph differential equations

Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results

Modified Variational Iteration Method for the Multi-pantograph Equation with Convergence Analysis

Abstract: In this paper, one effective modification of the variational iteration method is applied for finding the solution of the multi-pantograph equation. Moreover, convergence analysis for this method is discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method

On solving fuzzy delay differential equation using bezier curves

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem

Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms

Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations. In this paper, we derive a Jacobi-Gauss-Lobatto collocation method (J-GL-C) to solve numerically nonlinear time-delayed Burgers-type equations. The proposed technique is implemented in two successive steps. In the first one, we apply nodes of the Jacobi-Gauss-Lobatto quadrature which depend upon the two general parameters , and the resulting equations together with the two-point boundary conditions constitute a system of ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve a system of ODEs of second order in time. We present numerical results which illustrate the accuracy and flexibility of these algorithms

Optimal type-3 fuzzy system for solving singular multi-pantograph equations

In this study a new machine learning technique is presented to solve singular multi-pantograph differential equations (SMDEs). A new optimized type-3 fuzzy logic system (T3-FLS) by unscented Kalman filter (UKF) is proposed for solution estimation. The convergence and stability of presented algorithm are ensured by the suggested Lyapunov analysis. By two SMDEs the effectiveness and applicability of the suggested method is demonstrated. The statistical analysis show that the suggested method results in accurate and robust performance and the estimated solution is well converged to the exact solution. The proposed algorithm is simple and can be applied on various SMDEs with variable coefficients

Optimal Type-3 Fuzzy System for Solving Singular Multi-Pantograph Equations

In this study a new machine learning technique is presented to solve singular multi-pantograph differential equations (SMDEs). A new optimized type-3 fuzzy logic system (T3-FLS) by unscented Kalman filter (UKF) is proposed for solution estimation. The convergence and stability of presented algorithm are ensured by the suggested Lyapunov analysis. By two SMDEs the effectiveness and applicability of the suggested method is demonstrated. The statistical analysis show that the suggested method results in accurate and robust performance and the estimated solution is well converged to the exact solution. The proposed algorithm is simple and can be applied on various SMDEs with variable coefficients.publishedVersio