Search
Search Results
-
An isoparametric tangled finite element method for handling higher-order elements with negative Jacobian
This paper presents an isoparametric tangled finite element method (i-TFEM) method for handling tangled high order/curvilinear meshes. Tangled...
-
Differential Equations
In this chapter, the focus is on differential equations, which are equations involving unknown functions and their derivatives. These equations allow...
-
Governing Equations
This chapter presents the equations framing the tip streaming phenomenon. These equations provide the theoretical framework to analyze the...
-
Transmission Line Equations
Discuss the general solution of the transmission line equations and explore the meaning of a “one-dimensional wave.”
-
Modeling of heat conduction through rate equations
Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media....
-
Differential and Difference Equations
Differential and difference equations are topics that occur everywhere in applications of mathematics such as physics, engineering, stochastic...
-
Roots of Nonlinear Equations
When we encounter zeros or roots of a function f(x), it indicates that we are referring to finding the solutions of a scalar equation f(x) = 0. In...
-
Convolution Equations
The objective of this chapter is to show that the solution of ordinary differential equations, if based on distributions as opposed to functions, can...
-
Ordinary Differential Equations
Differential equations (It is assumed that a course in differential equations precedes the course in which this text is used. This chapter is meant...
-
Partial Differential Equations
The physical systems studied thus far have been described primarily by ordinary differential equations. We are now interested in studying phenomena...
-
Two new Painlevé integrable KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation
In this work, we develop two new (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS...
-
Solution of Algebraic Equations
Algebraic equations are routinely encountered while modeling problems in various areas of engineering. Finding the solution of such equations is also...
-
Additive Functional Equations
The chapter derives additive functional equation and obtains general solution of the additive functional equation. Moreover, the stability of...
-
Linear Equations and Inequalities
Basic linear equations and inequalities are the topic of this short chapter. Being the most common forms, due to the fact that in principle any...
-
Quadratic Functional Equations
This chapter is primarily based on works related to the stability of quadratic functional equations. It presents some important results concerning...
-
A Appendix: Introduction to Stochastic Differential Equations
In this appendix we bring some basic results concerning stochastic differential equations of the Ito type which systems with state-multiplicative...
-
Differential Form of Conservation Equations
The detailed structure of a flow field and its evolution over time are described by a system of partial differential equations that stem from the...
-
-
Reynolds Transport Theorem, Isentropic, Continuity, and Momentum Equations
This chapter introduces the key aerodynamic equations. Specifically, using Reynolds transport theorem the continuity and momentum equations are...
-
Elastoplastic Constitutive Equations
Elastic deformation is induced microscopically by the elastic deformations of the material particles themselves, exhibiting a one-to-one...