Haar Wavelet Method for Solving Stiff Differential Equations

Abstract

Abstract. Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered. Efficiency of the recommended method is demonstrated by means of four numerical examples, mostly taken from well-known textbooks.

Second Kind Chebyshev Wavelet Method for Solving System of Linear Differential Equations

“…we can get the approximate values of x(t), y(t), z(t) by inserting these values in (7). The absolute error of exact and approximate solution for M = 3, k = 2 using second kind Chebyshev wavelet method and Legendre wavelet method is given in Table 3.…”

“…Many authors have used wavelet related numerical and approximate methods to solve differential equations see ( [7] and [8]), integral equations [9], variational problems [10] etc.…”

A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

“…where p Γ ,i (x), p Λ,i ( y) are functions defined in (5) and (6), and Ψ(x, y) is a function satisfying the boundary conditions σ. The other derivatives can be directly determined by taking the derivatives of u(x, y).…”

“…By increasing the multiresolution parameter m, the accuracy of solution can be improved. Lepik adapted the method of Chen and Hsiao 1 to solve various types of differential equations such as nonlinear ODEs 3 , evolution equations 4 , integral equations 5 , higher-order ODEs 6 , and PDEs 3,7 . Lepik 7 proposed a procedure to solve PDEs by using the two-dimensional Haar wavelet and claimed that the proposed method was mathematically simple and computationally efficient for solving the diffusion and Poisson equations.…”

Efficiency and Accuracy of Numerical Solution of Laguerre's Differential Equation Using Haar Wavelet

“…In past literature [9,10,11,12,13,14,15], it have been claimed that the solution of differential equations by Haar wavelet methods are more accurate. In the present paper, we see that the above claims by various authors in the past is not true for Laguerre's equation, even though it has polynomial solutions.…”