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 corre
The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. This solution has been used to build up an exact Riemann solver implemented in...
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 ...
Maple’s symbolic solver uses state algorithm to solve algebraic equation problems, including F4 algorithm to calculate Gröbner and triangle set to decompose algorithm. Here, we obtain the coefficient solution with the help of Maple, (3.3)a=a,b=b,a1=−ba2a52p22,a2=a2,a3=−a2−a56...
When applying a solver of Diophantine equations to this system, it returns the solution 𝑐0=0,𝑐1=1,𝑐2=1,𝑐3=0,𝑐4=0,𝑐5=0,c0=0,c1=1,c2=1,c3=0,c4=0,c5=0, (6) which leads to the second-order recursive equation defining the Fibonacci sequence: 𝑎𝑛=0·1+...
∫ ′∫∑ ∫∫∫∑∏ ′′′ ラプラスベルヌーイ代入法線形完全 すべて表示 完全 進む 例 完全2xy−9x2+(2y+x2+1)dydx=0 完全2xy−9x2+(2y+x2+1)dydx=0,y(0)=3 完全2xy2+4=2(3−x2y)y′ ′
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 ...
- 1997 () Citation Context ...ed by an ODE solver. The same argument is valid for the zero dynamics. In the non minimum phase case it is however more complex to handle parameter variations and not even possible for all cases, see =-=[8, 9]-=-. 3.2 Handling of conditional functions...
I will then proceed to explain what steps the method actually carries out in solving the differential equation along with the high level programming language code, I used to write a simple Runge Kutta solver and the output of the code, given some basic differential equations. I will then end...
A local error of 10−40 has been requested from the differential equation solution. The numerical solution of eqs. (3.3) requires a boundary value for each Ik. In order to obtain these, we have used a high-order large-mass expansion, see e.g. [24], around z = 0. The expansion ...