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 ...

The giant planet Saturn was observed by XMM-Newton in September 2002. We present and analyse these XMM-Newton observations and compare our findings to the Chandra observations of Saturn. Contamination of the XMM-Newton data by optical light is found to be severe in the medium and thin filters, but with the thick filter all optical light is sufficiently blocked and the signal observed in the thi...

We present an Altered Jacobian Newton Iterative Method for solving nonlinear elliptic problems. Effectiveness of the proposed method is demonstrated through numerical experiments. Comparison of our method with Newton Iterative Method is also presented. Convergence of the Newton Iterative Method is highly sensitive to the initialization or initial guess. Reported numerical work shows the robustn...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...