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This question is an exact duplicate of: How can I get a numerical solution of coupled nonlinear ODEs? [on hold] The equations are and the initial conditions and boundary conditions are given are How I can get a numerical solution of coupled this system with Mathematica? 1 is problem 2 is values of A’s 3Read more

The equations are and the initial conditions and boundary conditions are given are How we can get Numerical solution of coupled Nonlinear ODE of eq 13, 14 and 15 using mathematica?Read more

In a field, if we require that all polynomials have at least one root, then it’s algebraically closed and all polynomials factor completely. In a ring, the same requirement implies that it’s an ACF, because linear polynomials need a root and this ensures multiplicative inverses. This raises the question, is there some other way aRead more

Let the nonlinear operator $ F:H\to H$ be weakly continuous on the separable Hilbert space $ H$ , i.e., if $ x_n\to x_0$ weakly then $ F(x_n)\to F(x_0)$ weakly in $ H$ . This nonlinear operator also admits local Lipschitz continuity in the strong sense. Now, consider a sequence $ x_n(t)\in C(0,T;H)$ weakly convergent inRead more

I am working in the traffic flow problem using the Lighthill-Whitham-Richards model together with the Greenshields equation. The equation of that model is this: $ $ \frac{\partial\rho}{\partial t}+v_{max} \left( 1- \frac{2\rho}{\rho_{max}}\right) \frac{\partial\rho}{\partial x}=0. $ $ The particular case in which I am having problems with the simulation is the case when a traffic light turnsRead more

I’m trying to obtain analytical solution of the following non-linear equation: Mathematica gave me two weird solutions: Can anyone help me to interpret these solutions? Why does 0 appear in the solution? Thanks!Read more

I am trying to solve an ODE which has the following form: $ $ \dfrac{\mathrm{d}y}{\mathrm{d}x} = \frac{Axy \ + \ By^2 \ + \ Cy}{Dxy \ + Ey \ +\ Fx \ + G}$ $ with an initial condition $ y(x_0) = y_0 \ $ . The approaches I could think of to solve thisRead more

Solve[x1*(1-x1^2-y1^2)-w*y1+e*(0.5*Q*(x1+x2)-x1)+h==0&y1*(1-x1^2-y1^2)+w*x1==0&x2*(1-x2^2-y2^2)-w*y2+e*(0.5*Q*(x1+x2)-x2)==0&y2*(1-x2^2-y2^2)+w*x2==0,{x1,y1,x2,y2}] I use this code in Mathematica to solve this coupled nonlinear set of equations, and want to find (x1,y1,x2,y2) analytically. But it can not return any value, the code is running …… for a long time . I tried several times, but the Mathematica can not give solution. I also use Reudce command ,Read more

I would like to state that this is related to a past question of mine which contained errors and now appears in the corrected form, with the erroneous one deleted and closed. In my research of linear algebra and optimization I have recently come across a problem related to the well-known low-rank optimization problem: GivenRead more

In my research of linear algebra and optimization I have recently come across a problem related to the well-known optimization problem: Given a constant matrix $ X\in\mathbb{R}^{n \times n}$ , $ $ \min_{A\in\mathbb{R}^{n\times k}, B\in\mathbb{R}^{k \times n}} \| X – A B \|_F$ $ Where the norm is the Frobenius norm. I was considering thisRead more