Solution Of Nonlinear Integro-differential Equations Research Articles

Statistical analysis for solution of non-linear integro-differential equation by using odinary and accerlated technique of Kamal-Adomian Decomposition

The integro-differential equations have a significant role in presenting the daily life phenomenon and researchers used different approaches for the solution of such problems. But it has been noticed that nonlinear integro-differential equations lack closed-form solutions. Consequently, approximate approaches are essential for determining approximate solutions to these models. The foremost goal of this research is to offer an innovative combined method by employing the Kamal transform and the Adomian decomposition method (ADM) for extracting analytical estimated, closed form, and numerical results of the non-linear differential-integral equations. The proposed method is named the Kamal Adomian Decomposition Method (KADM). To evaluate its efficiency and consistency the outcomes attained by the offered method are compared with the Laplace decomposition method which shows that our method is more efficient, that reveals the reliability of the presented method. The KADM will be used in the future to analyze new systems that emerge in many branches of science. The convergence analysis of the series of solutions is also presented. Furthermore, we provide some interesting non-trivial examples to show the validity of our main results.

Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

Objectives: Introduction to new numerical techniques to solve differential, difference, and integro-differential equations (IDEs) are always remaining the thrust area of research for many scientists over the centuries. The prime objective of this work is to contribute a new numerical technique to solve IDEs. Method: To address non-linear integro-differential equations, we computed an operational matrix of derivatives based on the Hosoya polynomial of the path graph in this work. Findings: Using the derived operational matrix, we have solved both Volterra and Fredholm integrodifferential equations. Taking suitable examples accuracy of the projected method is demonstrated in this paper in terms of a graphical representation of the absolute error. The results of the examples reveal that the projected method is a suitable method to solve IDEs. Novelty: The application of the Hosoya polynomial of path graph to solve integro-differential equations is a novel approach in the field of numerical analysis. Keywords: Volterra Integrodifferential equations; Fredhlom Integrodifferential equations; Graph theorypolynomials

Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type

<abstract><p>This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable conditions are developed to prove the proposed model's continues behavior which reflects the stable generation. At last, three test examples are presented to verify the established theoretical concepts.</p></abstract>

Nonlinear Integrodifferential Equations with Time Varying Delay

By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea.
 
 By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea.

Solution of non-linear integro-differential equations by using modified Laplace transform Adomian decomposition method

Solution of non-linear integro-differential equations by using modified Laplace transform Adomian decomposition method

Numerical solution of nonlinear integro-differential equations

The paper is devoted to the development of a numerical algorithm for solving nonlinear integro-differential equations based on the use of quadrature formulas. The Koltunov-Rzhanitsyn kernel with weakly singular features of the Abel type is used as a kernel. To conduct a computational experiment, a computer program was developed; the results obtained by this program are reflected in the form of tables and graphs. A test example was solved, and the obtained approximate numerical results were compared with exact solutions. The influence of nonlinearity and integral parts on the nature of oscillatory process of a viscoelastic body was investigated.

Existence and Uniqueness for the Controllability of a Dynamical System

In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.

Coupling Lévy measures and comparison principles for viscosity solutions

We prove new comparison principles for viscosity solutions of nonlinear integro-differential equations. The operators to which the method applies include but are not limited to those of Lévy–Itô type. The main idea is to use an optimal transport map to couple two different Lévy measures and use the resulting coupling in a doubling of variables argument.

On the comparative study integro – Differential equations using difference numerical methods

In this paper, we use the Adomian decomposition Sumudu transform method with the Pade approximant (ADST - PA method) to obtain closed form solutions of nonlinear integro-differential equations, and perform a comparative study between the present method and three different numerical methods, namely; the Adomian decomposition Sumudu transform method (ADSTM)), the homotopy perturbation method (HPM), and the variational iteration method (VIM). Our results show that in comparison with other existing methods, the (ADST - PA method) gives a better approximation for solving a large number of nonlinear integro-differential equations than existing methods.

One a way for Constructing Hybrid Methods with the Constant Coefficients and their Applied

As is known, the model problem for some scientific and technical problems is formulated with the help of the integro-differential equations of Volterra type of the second order. And for solving of such equations, numerical methods are mainly used. Numerical solution of nonlinear integro-differential equations of Volterra type has been studied relatively little. Therefore, here we consider the construction and application of numerical methods to solving Volterra’s nonlinear integro-differential equations. Here, are constructed specific methods which are applied to solving of the model problem and are proved the advantage of the proposed method.

EXISTENCE AND OSGOOD TYPE UNIQUENESS OF MILD SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATION WITH NONLOCAL CONDITION

The aim of the present paper is to study existence, Osgood type uniqueness and qualitative properties of mild solutions of nonlinear integrodifferential equation with nonlocal condition. The main tools employed in the analysis are based on the applications of the Leray-Schauder alternative, rely on a priori bounds of solutions and the well known Bihari’s integral inequality. AMS Subject Classification: 34A12, 37C25, 34B10

Existence of solutions for some classes of integro-differential equations via measure of noncompactness

In this present paper, we introduce a new measure of noncompactness on the space consisting of all real functions which are n times bounded and continuously differentiable on R+. As an application, we investigate the problem of the existence of solutions for some classes of the functional integral-differential equations which enables us to study the existence of solutions of nonlinear integro-differential equations. In our considerations we apply the technique of measures of noncompactness in conjunction with Darbo's fixed point theorem. Finally, we give some illustrative examples to verify the effectiveness and applicability of our results.

Existence of Mild and Classical Solutions of Nonlinear Integrodifferential Equation in Banach Space

Existence of Mild and Classical Solutions of Nonlinear Integrodifferential Equation in Banach Space

Nonlocal Cauchy Problem for Integrodifferential Equations of Sobolev Type in Banach Space

In this paper, we prove the existence and uniqueness of mild and strong solutions of nonlinear integrodifferential equations of Sobolev type in Banach space. The results are obtained by using compact semigroups and the Schauder fixed point theorem. Keywords: Mild and Strong solutions; Nonlocal condition; Integrodifferential equations; Compact semigroup; Schauder fixed point theorem. 2010 Mathematics Subject Classification: 45N05; 47H10; 47B38; 34G20

Positive Solutions for Nonlinear Integro-Differential Equations of Mixed Type in Banach Spaces

We establish some new existence theorems on the positive solutions for nonlinear integro-differential equations which do not possess any monotone properties in ordered Banach spaces by means of Banach contraction mapping principle and cone theory based on some new comparison results.

Numerical Solution of Nonlinear Integro-Differential Equations with Initial Conditions by Bernstein Operational Matrix of Derivative

In this paper, we present a practical matrix method for solving nonlinear Volterra-Fredholm integro-differential equations under initial conditions in terms of Bernstein polynomials on the interval [0,1]. The nonlinear part is approximated in the form of matrices’ equations by operational matrices of Bernstein polynomials, and the differential part is approximated in the form of matrices’ equations by derivative operational matrix of Bernstein polynomials. Finally, the main equation is transformed into a nonlinear equations system, and the unknown of the main equation is then approximated. We also give some numerical examples to show the applicability of the operational matrices for solving nonlinear Volterra-Fredholm integro-differential equations (NVFIDEs).

On Some Approximate Solutions of Nonlinear Integrodifferential Equation on Time Scales

The main objective of the paper is to study the approximate solutions of certain dynamic nonlinear integrodifferential equations on time scales which unifies the study of corresponding continuous and discrete version of the same. A new integral inequality with explicit estimates are used to establish the results.

Approximations of the nonlinear Volterra's population model by an efficient numerical method

In this paper, we apply the new homotopy perturbation method to solve the Volterra's model for population growth of a species in a closed system. This technique is extended to give solution for nonlinear integro-differential equation in which the integral term represents the total metabolism accumulated fromtime zero. The approximate analytical procedure only depends on two components. The newhomotopy perturbationmethodwas applied to nonlinear integro-differential equations directly and by converting the problem into nonlinear ordinary differential equation. We also compare this method with some other numerical results and show that the present approach is less computational and is applicable for solving nonlinear integro-differential equations and ordinary differential equations as well. Copyright © 2011 John Wiley & Sons, Ltd.

Flutter of a viscoelastic plate in a supersonic gas flow

The flutter of a viscoelastic plate in a supersonic gas flow is studied. A technique and algorithm for numerical solution of nonlinear integro-differential equations with weakly singular kernels are elaborated. The critical flutter speed of viscoelastic plates is determined

On gevrey asymptotics for some nonlinear integro-differential equations

We construct formal power series solutions of nonlinear integro-differential equations for given initial conditions which are holomorphic functions on a strip in the complex plane C. We give sufficient conditions on the shape of the equations and on the initial conditions under which there exist actual holomorphic solutions which are Gevrey asymptotic to the given formal series solutions with respect to the time variable on sectors in C. We get 1?Gevrey asymptotic expansions on sectors of opening less than ? but not 1?summability as it is the case for linear partial differential equations. Moreover, our approach yields global analytic solutions of these equations in both time and space variables.