In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

This paper provides a proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix. This theorem is also verified generally effective for all nonlinear polynomial algebraic system of equations. By using this relationship theorem, we give a Newton formula without requiring the evaluation of nonlinear function vector as well as a simple for...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

Abstract In this work, we investigate for finding exact solitary wave solutions of the (2 + 1)-dimensional Zoomeron equation and the Tzitzeica–Dodd–Bullough (TDB) equation by using the direct algebraic method. The direct algebraic method is promising for finding exact traveling wave solutions of nonlinear evolution equations in mathematical physics. The competence of the methods for constructin...

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BS...

We develop several tools to derive linear independent multivariate equations from algebraic S-boxes. By applying them to maximally nonlinear power functions with the inverse exponents, Gold exponents, or Kasami exponents, we estimate their resistance against algebraic attacks. As a result, we show that S-boxes with Gold exponents have very weak resistance and S-boxes with Kasami exponents have ...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

We describe the rif algorithm which uses a nite number of diierentiations and algebraic operations to simplify analytic nonlinear systems of partial diierential equations to what we call reduced involutive form. This form includes the integrability conditions of the system and satisses a constant rank condition. The algorithm is useful for classifying initial value problems for determined pde s...

By means of computerized symbolic computation and a modified extended tanhfunction method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission l...

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...