We present a heuristic solution for B-term approximation of 1-D discrete signals using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: best basis selection and greedy approximation. In addition, when approximating the same signal with different B constraints or error metrics, our solution also provides the flexibility of reducing overall computation time of appr...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted L and L∞ estimates. Furthermore, we establish the higher order asymptotic expansion of the solution. This means that we construct the nonlinear approximation of the global solution with respect to the weigh...

Catalytic isomerization of glucose to fructose by immobilized glucose isomerase in an aqueous-ethanol medium was studied. Using Michaelis-Menten equation and Haldane relationship, the main kinetic parameters were determined: Kmf, Vmf, Kmr, Vmr. By comparing the aqueous-ethanol medium with an aqueous solution, the measured values of Kmr and Kmf were increased in the aqueous-ethanol solution, whi...

This paper presents a fast approximation for the solution of the radiative transfer equation in inhomogeneous participating media. This scheme traces rays from the point light creating spherical wavefronts. While we march on a particular ray, we assume that other rays find similar material properties, which allows the solution of the diffusion equation for this ray. The proposed approximation o...

The Liouville-Green [or Wentzel-Kramers-Brillouin (WKB)] approximation for the two-dimensional cochlear mechanics problem disagrees with the finite-difference solution in the region after the response peak. This disagreement has left doubts about the validity of the Liouville-Green approximation, and has never been satisfactorily explained. In this paper, it is shown that the Liouville-Green ap...

In this paper, we study finite element approximations of the viscosity solution of the fully nonlinear Monge-Ampère equation, det(Du) = f (> 0) using the well-known nonconforming Morley element. Our approach is based on the vanishing moment method, which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and Feng in [15]. The vanishin...

In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this solution, exponents of the corresponding Lotka-Volterra variables have simple, time polynomial form. When approximation order tends to infinity obtained approx...

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...