Nonlinear evolution wave equations (NEEs) are partial differential equations (PDEs) involving first or second order derivatives with respect to time. Such equations have been intensively studied for the past few decades [1-3] and several new methods to solve nonlinear PDEs either numerically or analytically are now available. Hirota's bilinear method is a powerful tool for obtaining a wide clas...

In this paper, optimal control for linear partial differential algebraic equations (PDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the PDAE is transformed into a differential algebraic equations (DAE). Hence, the optimal control of PDAE can be found out by finding the optimal control of the corresponding DAE. The goal is to provide optimal control wit...

It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function ψ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium ...

the solution of a certain partial differential equation of the second order which is reduced by quadratures to a linear partial differential equation of the first order. The more complicated types of problems in the calculus of variations are examined in a similar manner. But in no type except the simplest are the differential equations which present themselves as necessary conditions of genera...

this paper presents the jeffery hamel flow of a non-newtonian fluid namely casson fluid. suitable similarity transform is applied to reduce governing nonlinear partial differential equations to a much simpler ordinary differential equation. variation of parameters method (vpm) is then employed to solve resulting equation. same problem is solved numerical by using runge-kutta order 4 method. a c...