Chapter III Approximate Solution of the Random Volterra Integral Equation and an Application to Population Growth Modeling

1974 ◽  
pp. 65-96
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Population Growth ◽  
Volterra Integral Equation ◽  
Growth Modeling

scholarly journals Computational Methods for Solving Linear Fuzzy Volterra Integral Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jihan Hamaydi ◽  
Naji Qatanani
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Numerical Methods ◽  
Volterra Integral Equation ◽  
Taylor Expansion ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Iteration Methods ◽  
Good Agreement

Two numerical schemes, namely, the Taylor expansion and the variational iteration methods, have been implemented to give an approximate solution of the fuzzy linear Volterra integral equation of the second kind. To display the validity and applicability of the numerical methods, one illustrative example with known exact solution is presented. Numerical results show that the convergence and accuracy of these methods were in a good agreement with the exact solution. However, according to comparison of these methods, we conclude that the variational iteration method provides more accurate results.

scholarly journals Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

2021 ◽  
Vol 54 (1) ◽  
pp. 11-24
Author(s):  
Atanaska Georgieva
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Homotopy Analysis Method ◽  
Volterra Integral Equations ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fuzzy Solution

Abstract The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.

scholarly journals THE COMPUTATIONAL EFFICIENCY OF WALSH APPROXIMATION FOR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS

2011 ◽  
Vol 04 (02) ◽  
pp. 263-270 ◽  
Author(s):  
S. Anderyance ◽  
M. Hadizadeh
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Volterra Integral Equation ◽  
Computational Efficiency ◽  
Numerical Scheme ◽  
Operational Matrix ◽  
Wavelet Packets ◽  
Walsh Functions ◽  
Two Dimensional ◽  
Operational Matrix Of Integration

In this research, we give details of a new numerical method for the approximate solution of a general two-dimensional Volterra integral equation, using the discontinuous wavelet packets e.g. Walsh functions. The double Walsh approximation we have adopted utilizes a simple robust numerical scheme for approximate solution of the equations. The two-dimensional operational matrix of integration for each subinterval [Formula: see text] is explicitly constructed, where m is a power of 2. Finally the reliability and efficiency of the proposed scheme are demonstrated by some numerical results.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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