in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

In computer graphics, the radiosity equation plays an important in obtaining realistic illumination. The size of the system generated when solving the radiosity equation can have very large order and consequently, the cost of solving this system can be quite large, both in computing time and memory. In this paper, we investigate the applicability and performance of some Krylov subspace methods ...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

The monotone iterative technique is applied to a class of nonlinear first order integro-differential equations in Banach spaces. First a linear system with a “small” nonlinear perturbation is solved using Banach’s Contraction Principle and the technique of Green’s function. Then based upon a comparison result, the existence of minimal and maximal solutions is proved.

A review of the authors’s results is given. Several methods are discussed for solving nonlinear equations F (u) = f , where F is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy principle for solving the equation is formulated and justified. Various versions of the Dynamical Systems Method (DSM) for solving the equation are formulated. T...

Student difficulties with the study of algebra have been well documented. The inability of many students to understand variables and formal symbolic manipulation act as a barrier to success in mathematics study. This report documents an intervention that uses a concrete approach to teaching algebra in a Year 9 class. Results indicate that much of the student struggle was associated with a lack ...