In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the d...

Most process models resulting from first principles consist of not only nonlinear differential equations but also contain nonlinear algebraic equations, resulting in nonlinear DAE systems. Since large-scale nonlinear DAE systems are too complex to be used for real-time optimization or control, model reduction of these types of models is a strategy that needs to be applied for online application...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

A theoretical framework for the stabilization of control systems defined by a class of nonlinear differential-algebraic equations is established. Assumptions are stated which guarantee that the nonlinear differential-algebraic equations can be described by a nonlinear control system defined on a smooth manifold. A procedure for obtaining a local state realization is developed. Conditions for lo...

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by...

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the d...

We study the instability of algebraic solitons for integrable nonlinear equations in one spatial dimension that include modified KdV, focusing NLS, derivative NLS, and massive Thirring equations. We develop the analysis of the Evans function that defines eigenvalues in the corresponding Lax operators with algebraically decaying potentials. The standard Evans function generically has singulariti...

Analysis of a laminated composite beam under impact by a rigid particle is investigated. The importance of this project is to simulate the impact of objects on small scale aerial structures. The stresses are considered uni- axial bending with no torsion loading. The first order shear deformation theory is used to simulate the beam. After obtaining kinematic and potential energy for a laminated ...