The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than ...
The aim of the manuscript is to present a new exact solver of nonlinear partial differential equations. The proposed technique is developed by extending the 6-model expansion method as a known method. The corresponding exact solutions are given in terms of Jacobi elliptic functions. Some new ...
For the simulation of both subsystems, a classical numerical solver, the explicit Euler method with a step size of δt=2ms, has been chosen. 2.1.2. Model-based pre-step stabilization method For this co-simulation, the subsystems are coupled in parallel with a model-based approach, the ...
. Exact equations relating second- and third-order structure functions are studied, as is an exact incompressibility condition on the second-order velocity ... HILL,REGINALD J. - 《Journal of Fluid Mechanics》 被引量: 104发表: 2002年 Existence results for third order nonlinear boundary value pro...
Next, it introduces Diofantos, an algorithm for discovering exact equations using a solver of linear Diophantine equations. 3.1. Task The task of discovering exact integer equations from data can be formalized as follows: Given observations of the values of the set of integer variables 𝑉={...
Gröbner basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under projections or rational maps. Maple’s symbolic solver uses state algorithm to solve algebraic equation problems, including F4 algorithm to ...
In this work, it is assumed that each transformation matrixTis an invertible square matrix with real values [25]. The transformed model equations can be deduced from Equation3by differentiation z→=Tx→|ddt⇒z→˙=Tx→˙=Tf→(x→,u→). ...
Connecting orbits of nonlinear differential equations have long been studied in the dynamical systems literature, generally in a setting involving perturba... CN Chen,SY Tzeng - 《Journal of Differential Equations》 被引量: 21发表: 2013年 LQ-optimal control of positive linear systems The LQ+ prob...
ACL can parameterize complex functions and z can be exactly recovered given z′: z_a = ({z'_a - \psi (z_b)})/{\Psi (z_b)} \label {eq:invert} (7) Noting the similarity of equations 6 and 7 to the simplified form of Eq. (2), we parallel this cons...
nonlinear differential equationssensitivity analysisseries (mathematics)/ exact Riemann problemnonlinear shallow-water equationsRiemann solvernonlinear fluid-flow problemsThe Riemann solver is the fundamental building block in the Godunov-type formulation of many nonlinear fluid-flow problems involving ...