scholarly journals Analytical Solution of System of Volterra Integral Equations Using OHAM

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Akbar ◽  
Rashid Nawaz ◽  
Sumbal Ahsan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Integral Equations ◽  
Function Method ◽  
Auxiliary Function ◽  
Volterra Integral Equations ◽  
Large Parameter ◽  
Reliable Technique ◽  
Present Technique ◽  
Optimal Homotopy Asymptotic Method

In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.

Numerical Algorithms of Optimal Complexity for Weakly Singular Volterra Integral Equations

2006 ◽  
Vol 6 (4) ◽  
pp. 436-442 ◽  
Author(s):  
A.N. Tynda
Keyword(s):  
Numerical Methods ◽  
Integral Equations ◽  
Numerical Algorithms ◽  
Volterra Integral Equations ◽  
Volterra Equations ◽  
Fredholm Integral Equations ◽  
Optimal Complexity ◽  
Weakly Singular ◽  
Different Types ◽  
Singular Kernels

AbstractIn this paper we construct complexity order optimal numerical methods for Volterra integral equations with different types of weakly singular kernels. We show that for Volterra equations (in contrast to Fredholm integral equations) using the ”block-by-block” technique it is not necessary to employ the additional iterations to construct complexity optimal methods.

XVI.—Dual Series Relations. III. Dual Relations Involving Trigonometric Series

1963 ◽  
Vol 66 (3) ◽  
pp. 173-184 ◽  
Author(s):  
R. P. Srivastav
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Integral Equations ◽  
Trigonometric Series ◽  
Analytical Solutions ◽  
Fredholm Integral Equation ◽  
Auxiliary Function

SynopsisThe methods developed in I, II of this series of papers are applied to a solution of a variety of dual series relations involving trigonometric series. In general the problem is reduced to one of solving (usually by numerical methods) a Fredholm integral equation of the second kind for an auxiliary function g(t), but for certain values of the parameters it is possible to obtain analytical solutions of the integral equations and these cases are considered in detail.

scholarly journals PROJECTION METHODS FOR INTEGRAL EQUATIONS IN EPIDEMIC

2002 ◽  
Vol 7 (2) ◽  
pp. 229-240 ◽  
Author(s):  
L. Hacia
Keyword(s):  
Mathematical Modeling ◽  
Numerical Methods ◽  
General Theory ◽  
Integral Equations ◽  
Projection Methods ◽  
Volterra Integral Equations ◽  
Temporal Development ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Spatio Temporal

In this paper numerical methods for mixed integral equations are presented. Studied equations arise in the mathematical modeling of the spatio‐temporal development of an epidemic. The general theory of these equations is given and used in the projection methods. Projection methods lead to a system of algebraic equations or to a system of Volterra integral equations. The considered theory is illustrated by numerical examples.

scholarly journals Optimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kind

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Jafar Biazar ◽  
Roya Montazeri
Keyword(s):  
Nonlinear Systems ◽  
Integral Equations ◽  
Asymptotic Method ◽  
Asymptotic Methods ◽  
Volterra Integral Equations ◽  
Optimal Homotopy Asymptotic Method ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, optimal homotopy asymptotic method (OHAM) and its implementation on subinterval, called multistage optimal homotopy asymptotic method (MOHAM), are presented for solving linear and nonlinear systems of Volterra integral equations of the second kind. To illustrate these approaches two examples are presented. The results confirm the efficiency and ability of these methods for such equations. The results will be compared to find out which method is more accurate. Advantages of applying MOHAM are also illustrated.

On Maxwell's equations in non-stationary media

2008 ◽  
Vol 366 (1871) ◽  
pp. 1781-1788 ◽  
Author(s):  
I Vorgul
Keyword(s):  
Analytical Solution ◽  
Plane Wave ◽  
Integral Equations ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Exact Analytical Solution ◽  
Charge Injection ◽  
Incident Field ◽  
Volterra Integral Equations ◽  
Numerical Investigations

Maxwell's equations formulated for media with gradually changing conductivity are reduced to Volterra integral equations. Analytical and numerical investigations of the equations are presented for the case of gradual splash-like change in conductivity. Splash-like change in medium parameters can model any discharge phenomena, growing plasma, charge injection, etc. Exact analytical solution for the resolvent is presented and different field behaviours are analysed for the incident field as a plane wave and as an impulse.

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