Approximate Solution Of The System Of Non-Linear Volterra Integro-Differential Equations

2008 ◽  
Vol 8 (1) ◽  
pp. 77-85 ◽  
Author(s):  
A. KHANI ◽  
M.M. MOGHADAM ◽  
S. SHAHMORAD
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Matrix Form ◽  
New Method ◽  
Numerical Computations ◽  
Non Linear ◽  
The Matrix ◽  
Computational Aspects

Abstract In this paper we develop a new method to find a numerical solution for the system of non-linear Volterra integro-differential equations (SNVE). To this end, we present our method based on the matrix form of SNVE. The corresponding unknown coefficients of our method have been determined by using the computational aspects of matrices. Finally the accuracy of the method has been verified by presenting some numerical computations.

scholarly journals Numerical solution of nonlinear system of integro-differential equations using Chebyshev wavelets

2015 ◽  
Vol 11 (2) ◽  
pp. 15-34
Author(s):  
H. Aminikhah ◽  
S. Hosseini
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Differential Equations ◽  
Numerical Solution ◽  
Chebyshev Wavelets ◽  
Linear And Nonlinear

Abstract This paper introduces an approach for obtaining the numerical solution of the linear and nonlinear integro-differential equations using Chebyshev wavelets approximations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with the exact solution. Comparison of the approximate solution with exact solution shows that the used method is effectiveness and practical for classes of linear and nonlinear system of integro-differential equations.

Numerical Solution for a System of Fractional Differential Equations with Applications in Fluid Dynamics and Chemical Engineering

2017 ◽  
Vol 15 (5) ◽  
Author(s):  
Bijil Prakash ◽  
Amit Setia ◽  
Shourya Bose
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Crucial Role ◽  
Chemical Engineering ◽  
Haar Wavelets ◽  
Fractional Differential

Abstract In this paper, a Haar wavelets based numerical method to solve a system of linear or nonlinear fractional differential equations has been proposed. Numerous nontrivial test examples along with practical problems from fluid dynamics and chemical engineering have been considered to illustrate applicability of the proposed method. We have derived a theoretical error bound which plays a crucial role whenever the exact solution of the system is not known and also it guarantees the convergence of approximate solution to exact solution.

Optimal Finite Analytic Methods

1982 ◽  
Vol 104 (3) ◽  
pp. 432-437 ◽  
Author(s):  
R. Manohar ◽  
J. W. Stephenson
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Linear Combination ◽  
Difference Equations ◽  
New Method ◽  
Linear Partial Differential Equations ◽  
Finite Difference Equations

A new method is proposed for obtaining finite difference equations for the solution of linear partial differential equations. The method is based on representing the approximate solution locally on a mesh element by polynomials which satisfy the differential equation. Then, by collocation, the value of the approximate solution, and its derivatives at the center of the mesh element may be expressed as a linear combination of neighbouring values of the solution.

Numerical Solution of the Beam Equation With Nonuniform Foundation Coefficient

1979 ◽  
Vol 46 (4) ◽  
pp. 901-904 ◽  
Author(s):  
M. Lentini
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
New Method ◽  
Beam Equation ◽  
Infinite Intervals

A new method for computing the solutions of the beam equation is given for the case of the problem of a pile. The method could be used for other problems where it is necessary to solve boundary-value problems for ordinary differential equations over semi-infinite intervals.

Analytical-Numerical Solution of Bending Problem of Thin Plates in Rubber Pad Bending

2011 ◽  
Vol 473 ◽  
pp. 190-197 ◽  
Author(s):  
M. Mehrara ◽  
Mohammad Javad Nategh
Keyword(s):  
Plastic Deformation ◽  
Differential Equations ◽  
Numerical Solution ◽  
Process Planning ◽  
Indentation Depth ◽  
New Method ◽  
Thin Plates ◽  
Roll Bending ◽  
Bending Radius ◽  
Plastic Zones

The bending of plates on rubber pad is a relatively new method used for roll bending of thin plates in recent years. In the present work the problem of plastic deformation of thin plates was analyzed. The governing differential equations for the plate’s elastic and plastic zones were derived. An analytical-numerical solution to these equations was subsequently presented. In addition, the equations were solved for a given problem and the effect of indentation depth of plate on its bending radius was investigated. A relationship has been proposed to correlate these parameters. This relationship is a powerful tool in controlling the process and process planning. This tool helps the operator set the indentation depth to a predefined amount in order that the plate to be bent by a given radius, without any try and error effort. The results were verified by experiment.

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