Fatih Bulut

A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers’ equation

In this paper, we investigate the numerical solutions of one dimensional modified Burgers’ equation with the help of Haar wavelet method. In the solution process, the time derivative is discretized by finite difference, the nonlinear term is linearized by a linearization technique and the spatial discretization is made by Haar wavelets. The proposed method has been tested by three test problems. The obtained numerical results are compared with the exact ones and those already exist in the literature. Also, the calculated numerical solutions are drawn graphically. Computer simulations show that the presented method is computationally cheap, fast, reliable and quite good even in the case of small number of grid points.

Wavelets in Field Theory

We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large-volume and short-distance cutoffs, has natural partitions of unity, and the basis functions are all related to the fixed point of a linear renormalization group equation.

A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations

In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrodinger–Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank–Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.

Wavelet methods in the relativistic three-body problem

We discuss the use of wavelet bases to solve the relativistic three-body problem in momentum space. We address the treatment of the moving singularities that appear in the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean interaction-independent treatment of the scattering singularities that does not require any subtractions.

Multiresolution decomposition of quantum field theories using wavelet bases

We investigate both theoretical and computational aspects of using wavelet bases to decouple physics on different scales in quantum field theory.

An alternative approach to compute wavelet connection coefficients

Abstract In this paper we present a step by step algorithm to compute the wavelet connection coefficients using Daubechies wavelets. We address the treatment of scaling function derivatives which has a potential to simplify the computation of connection coefficients. We describe the evaluation of the integrals involving products of Daubechies wavelets and their derivatives. These connection coefficients are necessary for the wavelet-Galerkin approximation of differential or integral equations.

Multi-scale Methods in Quantum Field Theory

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.

A haar wavelet approximation for two-dimensional time fractional reaction–subdiffusion equation

In this study, we established a wavelet method, based on Haar wavelets and finite difference scheme for two-dimensional time fractional reaction–subdiffusion equation. First by a finite difference approach, time fractional derivative which is defined in Riemann–Liouville sense is discretized. After time discretization, spatial variables are expanded to truncated Haar wavelet series, by doing so a fully discrete scheme obtained whose solution gives wavelet coefficients in wavelet series. Using these wavelet coefficients approximate solution constructed consecutively. Feasibility and accuracy of the proposed method is shown on three test problems by measuring error in

Numerical Solutions of Regularized Long Wave Equation By Haar Wavelet Method

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