A WAVELET COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF POPULATION DIFFERENTIAL EQUATION

2019 ◽  
Author(s):  
Amjad Alipanah ◽  
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Collocation Method ◽  
Wavelet Collocation Method

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

scholarly journals A New Efficient Method for the Numerical Solution of Linear Time-Dependent Partial Differential Equations

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 70
Author(s):  
Mina Torabi ◽  
Mohammad-Mehdi Hosseini
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Efficient Method ◽  
Linear Time ◽  
Time Dependent ◽  
Time Step ◽  
Partial Differential ◽  
Wavelet Collocation Method ◽  
One Step ◽  
The One

This paper presents a new efficient method for the numerical solution of a linear time-dependent partial differential equation. The proposed technique includes the collocation method with Legendre wavelets for spatial discretization and the three-step Taylor method for time discretization. This procedure is third-order accurate in time. A comparative study between the proposed method and the one-step wavelet collocation method is provided. In order to verify the stability of these methods, asymptotic stability analysis is employed. Numerical illustrations are investigated to show the reliability and efficiency of the proposed method. An important property of the presented method is that unlike the one-step wavelet collocation method, it is not necessary to choose a small time step to achieve stability.

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