Solving of nonlinear Fredholm integro-differential equation in a complex plane with rationalized Haar wavelet bases

2019 ◽  
Vol 12 (04) ◽  
pp. 1950055 ◽  
Author(s):  
Majid Erfanian ◽  
Hamed Zeidabadi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Approximate Solution ◽  
Integral Operator ◽  
Complex Plane ◽  
Haar Wavelet ◽  
Banach Fixed Point Theorem ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Rationalized Haar Wavelet

Everyone knows about the complicated solution of the nonlinear Fredholm integro-differential equation in general. Hence, often, authors attempt to obtain the approximate solution. In this paper, a numerical method for the solutions of the nonlinear Fredholm integro-differential equation (NFIDE) of the second kind in the complex plane is presented. In fact, by using the properties of Rationalized Haar (RH) wavelet, we try to give the solution of the problem. So far, as we know, no study has yet been attempted for solving the NFIDE in the complex plane. For this purpose, we introduce the continuous integral operator and real valued function. The Banach fixed point theorem guarantees that, under certain assumptions, the integral operator has a unique solution. Furthermore, we give an upper bound for the error analysis. An algorithm is presented to compute and illustrate the solutions for some numerical examples.

The approximate solution of nonlinear Fredholm implicit integro-differential equation in the complex plane

2021 ◽  
Author(s):  
Samir Lemita ◽  
Sami Touati ◽  
Kheireddine Derbal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Approximate Solution ◽  
Integral Operator ◽  
Complex Plane ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Numerical Process

This paper’s purpose is to study the nonlinear Fredholm implicit integro-differential equation in the complex plane, where the term implicit integro-differential means that the derivative of unknown function is founded inside of the integral operator. Initially, according to Banach fixed point theory, we ensure that the equation has a unique solution under particular conditions. However, we exhibit a numerical process based on the conjunction between Nyström and Picard methods, for the sake of approximating solutions of this equation. In addition to that, the convergence analysis of this numerical process is demonstrated, and some illustrated numerical examples are presented.

scholarly journals Controllability Analysis for Impulsive Integro-differential Equation via AB Fractional Derivative

2021 ◽  
Author(s):  
KALIMUTHU KALIRAJ ◽  
E. Thilakraj ◽  
Ravichandran C ◽  
Kottakkaran Nisar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Theorem ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Integro Differential Equation

In this work, we analyse the controllability for certain classes of impulsive integro - differential equations(IIDE) of fractional order via Atangana Baleanu derivative involving finite delay with initial and nonlocal conditions using Banach fixed point theorem.

scholarly journals Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Integrodifferential Equation ◽  
Order Derivative ◽  
Parametric Form ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
New Iterative Method

Thenth-order derivative fuzzy integro-differential equation in parametric form is converted to its crisp form, and then the new iterative method with a reliable algorithm is used to obtain an approximate solution for this crisp form. The analysis is accompanied by numerical examples which confirm efficiency and power of this method in solving fuzzy integro-differential equations.

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

scholarly journals A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Hossein Daliri Birjandi ◽  
Jafar Saberi-Nadjafi ◽  
Asghar Ghorbani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Iteration Method ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Collocation Technique ◽  
Computational Work ◽  
Novel Method

An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.

scholarly journals Multivalued Problems, Orthogonal Mappings, and Fractional Integro-Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
R. K. Sharma ◽  
Sumit Chandok
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Existence Of Solution ◽  
Point Problem ◽  
Contraction Mappings ◽  
Integro Differential Equation

In this manuscript, we propose some sufficient conditions for the existence of solution for the multivalued orthogonal ℱ -contraction mappings in the framework of orthogonal metric spaces. As a consequence of results, we obtain some interesting results. Also as application of the results obtained, we investigate Ulam’s stability of fixed point problem and present a solution for the Caputo-type nonlinear fractional integro-differential equation. An example is also provided to illustrate the usability of the obtained results.

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