Solution Of Volterra Integro-differential Equations Research Articles

Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations

Radial kernel interpolation is an advanced method in approximation theory for the construction of higher order accurate interpolants for scattered data up to higher dimensional spaces. In this manuscript, we formulate a radial kernel collocation approach for solving problems involving the Volterra integro-differential equations using two radial kernels: The Generalized Multi-quadrics and the linear Laguerre-Gaussians. This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. Two examples were used to illustrate the process; the numerical results are shown as tables and graphs. MATLAB 2018a was employed in the process.

A multistep collocation method for approximate solution of Volterra integro-differential equations of the third kind

A multistep collocation method for approximate solution of Volterra integro-differential equations of the third kind

AN EFFECTIVE COMPUTATIONAL APPROACH BASED ON HERMITE WAVELET GALERKIN FOR SOLVING PARABOLIC VOLTERRA PARTIAL INTEGRO DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS

In this research article Hermite wavelet based Galerkin method is developed for the numerical solution of Volterra integro-differential equations in onedimension with initial and boundary conditions. These equations include the partial differential of an unknown function and the integral term containing the unknown function which is the memory of the problem. Wavelet analysis is a recently developed mathematical tool in applied mathematics. For this purpose, Hermit wavelet Galerkin method has proven a very powerful numerical technique for the stable and accurate solution of giving boundary value problem. The theorem of convergence analysis and compare some numerical examples with the use of the proposed method and the exact solutions shows the efficiency and high accuracy of the proposed method. Several figures are plotted to establish the error analysis of the approach presented.

Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A Collocation Method Based on Euler and Bernoulli Polynomials for the Solution of Volterra Integro-Differential Equations

A class of two-step collocation methods for Volterra integro-differential equations

A new class of two-step collocation methods for the numerical solution of Volterra integro-differential equations is proposed. These methods are obtained by using the collocation points in the current and previous subintervals in order to obtain methods with desirable convergence order and good stability properties. The derivation of the proposed methods together with their convergence and stability analysis are described. The theoretical results and efficiency of the methods are confirmed with some numerical experiments.

Asymptotic behavior of solutions of Volterra integro-differential equations with and without retardation

Asymptotic stability, uniform stability, integrability, and boundedness of solutions of Volterra integro-differential equations with and without constant retardation are investigated using a new type of Lyapunov–Krasovskii functionals. An advantage of the new functionals used here is that they eliminate using Gronwall’s inequality. Compared to related results in the literature, the conditions here are more general, simple, and convenient to apply. Examples to show the application of the theorems are included.

Correct Solvability and Exponential Stability for Solutions of Volterra Integro-Differential Equations

Correct Solvability and Exponential Stability for Solutions of Volterra Integro-Differential Equations

Some Theorems in Existence, Uniqueness and Stability Solutions of Volterra Integro-Differential Equations of the First Order

Some Theorems in Existence, Uniqueness and Stability Solutions of Volterra Integro-Differential Equations of the First Order

EXISTENCE, UNIQUENESS AND STABILITY SOLUTIONS OF VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH RETARDED ARGUMENT AND SYMMETRIC MATRICES

In this study, we investigate the existence, uniqueness, and stability solutions of Volterra integrodifferential equations with retarded argument and symmetric matrices. The Picard approximation method and Banach fixed point theorem have been used in this study. Theorems on the existence and uniqueness of a solution are established under some necessary and sufficient conditions on closed and bounded domains (compact spaces).

Numerical Solution of Volterra Integro-Differential Equations with Linear Barycentric Rational Method

In this article, we study linear barycentric rational method (LBM) to solve one-order Volterra integro-differential equations. With the help of linear barycentric rational interpolation, the matrix form of Volterra integro-differential equations is obtained. Then the convergence rate of LBM for solving one-order integro-differential equation is proved. Further more, Volterra integro-differential equation systems is also solved by the linear barycentric rational method. At last, several examples are presented to valid our theoretical analysis.

Correct solvability and representation of the solutions of Volterra integro-differential equations with exponential-fractional kernels

For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.

Collocation method for approximate solution of Volterra integro-differential equations of the third-kind

In this paper, we have adapted the collocation method for solving a special class of Volterra integro-differential equations of the third-kind. Structure of the method and its applicability for proposed equations have been presented. Moreover we have investigated the solvability and convergence analysis of the method. Also some numerical examples are provided to illustrate the theoretical results.

Correct Solvability and Representation of Solutions of Volterra Integrodifferential Equations with Fractional Exponential Kernels

For abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space, the correct solvability of initial value problems is studied and the spectral analysis of operator functions being symbols of these equations is performed. This makes it possible to represent strong solutions of the equations under consideration as series in exponentials corresponding to spectral points of the operator functions. The equations in question are abstract forms of linear partial integrodifferential equations arising in the theory of viscoelasticity and in a number of other important applications.

Numerical Solution of Volterra Integro-Differential Equations Using Improved Runge-Kutta Methods

In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the integral operator in Volterra integro-differential equation is approximated using quadrature rule and Lagrange interpolation polynomials. To illustrate the efficiency of proposed methods, the test problems are carried out and the numerical results are compared with existing third and fourth order classical Runge-Kutta method with 3 and 4 stages, respectively. The numerical results showed that the Improved Runge-Kutta method by achieving the higher accuracy performed better results than existing methods.

Approximate solution of linear Volterra integro-differential equation by using cubic B-spline finite element method in the complex plane

So far, there are no any publications for solving and obtaining a numerical solution of Volterra integro-differential equations in the complex plane by using the finite element method. In this work, we use the linear B-spline finite element method (LBS-FEM) and cubic B-spline finite element method (CBS-FEM) for solving this equation in the complex plane. We also discuss the error and convergence of the method. Furthermore, we give some numerical examples to substantiate efficiency of the proposed method.

Weyl-almost periodic solutions and asymptotically Weyl-almost periodic solutions of abstract Volterra integro-differential equations

The main purpose of this article is to investigate Weyl-almost periodic solutions and asymptotically Weyl-almost periodic solutions of abstract Volterra integro-differential equations and inclusions. The class of asymptotically Weyl-almost periodic functions that we introduce here seems not to have been considered elsewhere, even in the scalar-valued case. We analyze the Weyl-almost periodic and asymptotically Weyl-almost periodic properties of convolution products and various types of degenerate solution operator families subgenerated by multivalued linear operators.

Numerical solutions of Volterra integro-differential equations using General Linear Method

In this paper, a third order General Linear Method for finding the numerical solution of Volterra integro-differential equation is considered. The order conditions of the proposed method are derived based on techniques of B-series and 'rooted trees'. The integral operator in Volterra integro-differential equation approximated using Simpson's rule and Lagrange interpolation is discussed. To illustrate the efficiency of third order General Linear Method, we compare the method with a third order Runge-Kutta method.