Solving Two-Dimensional Nonlinear Volterra Integral Equations Using Rationalized Haar Functions in the Complex Plane

2020 ◽  
Vol 12 (3) ◽  
pp. 409-415
Author(s):  
Majid Erfanian ◽  
Hamed Zeidabadi ◽  
Rohollah Mehri
Keyword(s):  
Integral Equations ◽  
Order Of Convergence ◽  
Computational Algorithm ◽  
Numerical Solutions ◽  
Haar Wavelet ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Wavelet Method ◽  
Haar Functions ◽  
Banach Theorem

In this work, two-dimensional rational Haar wavelet method has been used to solve the twodimensional Volterra integral equations. By using fixed point Banach theorem we achieved the order of convergence and the rate of convergence is O(n(2q)n). Numerical solutions of three examples are presented by applying a simple and efficient computational algorithm.

scholarly journals An operational Haar wavelet method for solving fractional Volterra integral equations

2011 ◽  
Vol 21 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Habibollah Saeedi ◽  
Nasibeh Mollahasani ◽  
Mahmoud Moghadam ◽  
Gennady Chuev
Keyword(s):  
Integral Equations ◽  
Fractional Integration ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Volterra Integral Equations ◽  
Algebraic Equations ◽  
Global Error Bound ◽  
Wavelet Method ◽  
Haar Wavelet Method ◽  
Abel Integral Equations

An operational Haar wavelet method for solving fractional Volterra integral equationsA Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

Approximate solutions of nonlinear two‐dimensional Volterra integral equations

2021 ◽  
Author(s):  
Sumbal Ahsan ◽  
Rashid Nawaz ◽  
Muhammad Akbar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equations ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Two Dimensional
Sign in / Sign up

Export Citation Format

Share Document