This paper deals with the construction of analytic-numerical solutions with a priori error bounds for systems of the type ut = Auxx, u(0; t) + ux(0; t) = 0, Bu(1; t) + Cux(1; t) = 0, 0¡x¡ 1; t ¿ 0, u(x; 0) = f(x). Here A, B, C are matrices for which no diagonalizable hypothesis is assumed. First an exact series solution is obtained after solving appropriate vector Sturm–Liouville-type problems....

A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method MLADM has been proposed for solving the model for HIV infection of CD4 T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method LADM with multistep approach. Fourth-order Runge-Kutta method RK4 is used to evaluate the effectiveness of the proposed...

Abstract In this paper, we use new parametic formof fuzzy numbers and convert a system of fuzzy integral equations to two system of integral equations in crisp. Then we solve a system of fuzzy integral equations by means of an analytic technique, namely the homotopy analysis method (HAM). Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. The res...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

The solution to the nonlinear output regulation problem requires one to solve a first-order partial differential equation, known as the Francis–Byrnes–Isidori equations. In this paper, we propose a method to compute approximate solutions to the Francis–Byrnes–Isidori equations when the zero dynamics of the plant are hyperbolic and the exosystem is two dimensional. With our method, we are able t...

In this paper an analytic approach is devised to represent, and study the behavior of, nonlinear dynamic chaotic Genesio system using general nonlinear modal representation. In this approach, the original nonlinear ordinary differential equations (ODEs) of model transforms to a sequence of linear timeinvariant ODEs. By solving the proposed linear ODEs sequence, the exact solution of the origina...

We obtain a closed form analytic solution for the Dual Phase Lagging equation. This equation is a linear, time-independent partial differential equation modeling the heat distribution in a thin film. The spatial domain is of micrometer and nanometer geometries. We show that the solution is described by a semigroup, and obtain a basis of eigenfunctions. The closure of the set of eigenvalues cont...

An exact analytic solution for the dynamics of vortex pairs is obtained for rapid temperature quenches of a superfluid film starting from the line of critical points below the critical temperature T(KT). An approximate solution for quenches at and above above T(KT) provides insights into the origin of logarithmic transients in the vortex decay, and is in general agreement with recent simulation...

Computing irradiance analytically from polygonal luminaires in polygonal environments has proven effective for direct lighting applications in diffuse radiosity environments. Methods for analytic integration have traditionally used edge-based solutions to the irradiance integral; our previous work presented a vertex-based analytic solution, allowing irradiance to be computed incrementally by ra...

In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate soluti...