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We propose a new class of SBVPs which deals with exothermic reactions. We also propose four computationally stable methods to solve singular nonlinear BVPs by using Hermite wavelet collocation which are coupled with Newton's…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
As we know differential equations are very useful for electrical engineers to solve a variety of problems like: voltage across a capacitor, input versus output voltage, etc. Therefore, the goal of this paper is to find the solutions of…
In this article, we introduce a semi-orthogonal tribonacci wavelet and develop a semi-orthogonal tribonacci wavelet collocation method, offering an effective numerical method for solving a class of non-linear singular BVPs.
In recent years some attempts have been done to relate the RBF with wavelets in handling high dimensional multiscale problems. To the author's knowledge, however, the orthonormal and bi-orthogonal RBF wavelets are still missing in the…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of…
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…
In this work we present Haar wavelet collocation method and solve the following class of system of Lane-Emden equation defined as \begin{eqnarray*} -(t^{k_1} y'(t))'=t^{-\omega_1} f_1(t,y(t),z(t)),\\ -(t^{k_2} z'(t))'=t^{-\omega_2}…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this paper we consider invariant formulation of nonlinear (Lagrangian…
The Haar wavelet based quasilinearization technique for solving a general class of singular boundary value problems is proposed. Quasilinearization technique is used to linearize nonlinear singular problem. Second rate of convergence is…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…