An adaptive numerical method for solving partial differential equations is developed. The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O(N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The treatment o...

impact of effluent discharge from aquaculture facilities is a growing concern among policy makers. Since 1974, the United States Environmental Protection Agency (EPA) has regulated discharge of pollutants to waters of the United States under authority of the National Pollutant Discharge Elimination System (NPDES) permit. In some states, the NPDES permits have been applied to effluents from aqua...

The lattice Boltzmann equation (LBE) method is a promising technique for simulating fluid flows and modeling complex physics in fluids, and can be modified for solving general nonlinear partial differential equations (NPDEs). The LBE method has recently attracted more and more attention since it may help us to better understand the mechanisms of the complicated physical phenomena and dynamic pr...

In this paper the physical meaning of a nonlinear partial differential equation (nPDE) of the fourth order relating to wave theory is deduced to the first time. The equation under consideration belongs to a class of less studied nPDEs and an explicit physical meaning is not known until now. This paper however bridges the gap between some known results and a concrete application concerning wave ...

in this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. periteration this method requires three evaluations of the function and one evaluation of its first derivative. a general error analysis providing the eighth order of convergence is given. several numerical examples are given to illustrate the efficiency and performance of the new ...

in this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. the sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. then, the newton-raphson method is used for solving these sets of algebraic equations. to present ability ...

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...