Nowadays the semiconductor devices in an electrical circuit are modelled by equivalent circuits containing basic network elements described by algebraic and ordinary differential equations. But the correct adjustment of these circuits has become a very difficult task for the network design. In [1] a new model for electrical circuits containing semiconductor devices is proposed. There the differ...

Backward stochastic differential equations (BSDEs) were introduced by Pardoux and Peng [6], and it was shown in various papers that stochastic differential equations (SDEs) of this type give a probabilistic representation for the solution (at least in the viscosity sense) of a large class of system of semi-linear parabolic partial differential equations (PDEs). A new class of BSDEs, called back...

In this paper, we prove the convergence of the vortex blob method for a family of nonlinear evolutionary partial differential equations (PDEs), the so-called b-equation. This kind of PDEs, including the Camassa-Holm equation and the Degasperis-Procesi equation, has many applications in diverse scientific fields. Our convergence analysis also provides a proof for the existence of the global weak...

In this work we are interested in the numerical solution of a coupled model of differential algebraic equations (DAEs) and partial differential equations (PDEs). The DAEs describe the behavior of an electrical circuit that contains semiconductor devices and the partial differential equations constitute drift-diffusion equations modeling the semiconductor devices in the circuit. After space disc...

Conditional expected values in Markov chains are solutions to a set of associated backward differential equations, which may be ordinary or partial depending on the number of relevant state variables. This paper investigates the validity of these differential equations by locating the points of non-smoothness of the state-wise conditional expected values, and it presents a numerical method for ...

Fourier spectral methods achieve exponential accuracy both on the approximation level and for solving partial differential equations (PDEs), if the solution is analytic. For linear PDEs with analytic but discontinuous solutions, Fourier spectral method produces poor pointwise accuracy, but still maintains exponential accuracy after post-processing [7]. In this paper, we develop a technique to r...

A constructive method is developed to obtain optimal sensor and actuator locations for inverse optimal state estimation and control of a class of linear distributed parameter systems (DPSs). Given the inverse optimal state estimators and controllers for linear DPSs developed by the first author recently, it is shown that the performance index for optimal locations of sensors and actuators is th...

The modified method of simplest equation is applied to the extended Korteweg de Vries equation and to generalized Camassa Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh equation are used as simplest equations. Some of the obtained solutions correspond to surface water wav...

we present here, a haar wavelet method for a class of third order partial dierentialequations (pdes) arising in impulsive motion of a flat plate. we also, present adomaindecomposition method to find the analytic solution of such equations. efficiency andaccuracy have been illustrated by solving numerical examples.

An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The special case of a general that produces pre-symplectic operator non-gradient adjoint-symmetry. These formulas are illustrated by several examples linear PDEs integrable nonlinear PDEs. Addit...