Differential equation

function of a single independent variable. This reduces the partial differential equation to a system of ordinary differential equations, each being a function of a single independent variable. For the transient conduction in a plain wall, the dependent variable is the solution function θ(X, F0), which is expressed in terms of θ(X, F0) = F(X)G(t), and the application of this method results in to the two ordinary differential equations, one in terms of X and the other one in F0. Now we demonstrate

\cite{212,213} and Zhang et al. \cite{214} adopted the local discontinuous Galerkin (LDG) method to solve convection diffusion equations and analyzed the corresponding superconvergence properties. On the other hand, non-symmetric discontinuous Galerkin method with interior penalty (the NIPG method), originally designed for elliptic equations, is analyzed by Zarin and Roos \cite{87} for convection–diffusion problems with parabolic layers. A disadvantage of DG method is that the method

Chaos Theory Explained “Traditionally, scientists have looked for the simplest view of the world around us. Now, mathematics and computer powers have produced a theory that helps researchers to understand the complexities of nature. The theory of chaos touches all disciplines.” -Ian Percival, The Essence of Chaos Part I: The Basics of Chaos. Watch a leaf flow down stream; watch its behavior within the water… Perhaps it will sit upon the surface, gently twirling along

Introduction Many physical phenomena in stationary condition such as electrical and magnetic potential, heat conduction, fluid flow and elastic problems in static condition can be described by elliptic partial differential equations (EPDE). The EPDE does not involve a time variable, and so describes the steady state of problems. A linear EPDE has the general form as presented in Eq. (1), where a,b,c are coefficient functions, the term f is a source (excitation) function and u is the unknown variable

The movie Hidden Figures is based on the remarkable true story of African American women working for NASA in Hampton, Virginia 1961. With all their hard work and determination, they did the calculations and equations for the shuttle launches of Friendship 7, Apollo 11, and other Space missions. One out of these women was a brilliant mathematician named Katherine Gobel- Johnson. As a young child, Gobel she was recognized for her high intellect and was recommended to an alternative school so they can

The determintaion for seeking my future in Structural Engineering comes from my interest in Structures after I joined undergraduate studies in Civil Engineering at Kathmandu University. I’d found my interest growing already in Civil Engineering when I was in high school. I was following works of my brother while he was studying Civil engineering. I could understand and draw Plan and sections before I was got enrolled in undergraduate studies. During my undergraduate studies, I particularly enjoyed

summary on the intellectual merits and broader impact of the project. The PI initiates a new approach (in items 2,5, 6), using the precise large time asymptotic behavior of solutions of a parabolic equation to study the geometric property of K manifolds, and to solve the Poincar Lelong equation. The method is effective in proving sharp and optimal result. The method reminisces the celebrated ergodic theorem of Birkhoff which connects the space average of a continuous function on the phase

when changes in any system component occur. As already mentioned, distributed (modularized) models are solved by a set of partial differential equations due to all the dependent variables consist of more than one independent variable. However, these equations can be homogeneous or non-homogenous (inhomogeneous) equations. In practice, the solution of a homogeneous equation with the appropriate boundary conditions illustrates the behavior of the system after it has been properly set in motion and then

On contrary flexible robot position is not constant and hence partial differential equation is used to represent the distributed nature of position. Further due to sudden change in payload there may be a large variation in manipulator parameters. Thus control with constant gain controllers is difficult and adaptive methods must be

A flat plate solar collector has a dynamic behaviour in response to variations in the intensity of solar radiation at different times of the day and also variations in weather conditions. The characteristics governing the input-output behaviour of a flat plate collector can be described by a mathematical model which serves as a prerequisite for simulation and control. The steady state and transient characteristics of flat plate solar collectors have been studied in \cite{Hilmer1999Solar,Dhariwal2005Solar