Questions tagged [wave-equation]

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Solving a 3+1D Wave Equation

I am having some problems with finding the solution to the magnetic field, B[x,y,z,t]. Is there anything I can change to my code to obtain a solution of B[x,y,z,t] with the initial conditions and ...
-3 votes
1 answer
102 views

differential wave equations [closed]

By seeking a solution of ∂u ∂t = c 2 ∂ 2u ∂x 2 in the form u(x,t) = X(x)T(t), obtain and solve ordinary differential equations satisfied by X(x) and T(t). Hence write down possible solutions for u(x,t)...
2 votes
1 answer
74 views

Solving equation using mathematica

How I can solve the equation : $$R -\tan^{-1}[(m1/m3)*(k3/k1)] - \tan^{-1}[(m1/m2)*(k2/k1)]=0$$ I tried on it using findroot as following : ...
2 votes
2 answers
579 views

How should I define the boundary conditions of free end and fixed end scenarios for 1D Wave Equation?

The 1D wave equation is $$\frac{\partial^2 u(x,t)}{\partial t^2} = c^2 \frac{\partial^2 u(x,t)}{\partial x^2}$$ where $c$ is the wave speed, $c^2=E/\rho$, $E$ is the Young's modulus and $\rho$ is the ...
1 vote
2 answers
180 views

Solving equation by mathematica and Finding value of b in an equation

I have an equation and I have tried solving it to find values of b but it doesn't give me any values The equation that I have tried to solve is : ...
4 votes
2 answers
554 views

Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
3 votes
1 answer
253 views

Simulating a gaussian pulse for the wave equation

In the process of investigating diffraction of waves, I am starting with a simple problem consisting in injecting a gaussian pulse at the boundary x=0 of a square domain and then solving the wave ...
0 votes
1 answer
71 views

How do I add a velocity boundary condition with specific time period

I have a wave equation for displacement and velocity, I want to add this boundary condition $v(x=0,\,t>0)=1$ My mathematica code is ...
3 votes
1 answer
240 views

Half-absorbing boundary conditions

I'm trying to solve the spherically symmetric wave equation $$0 = (\partial_t^2 - \partial_r^2 + 1)\phi(t,r)\,,$$ where $\phi(t,0) = 0$. Without doing anything fancy, we can solve this equation "...
1 vote
2 answers
408 views

Show resonance with wave equation numerically

Assume I have a one-dimensional medium of length $L$ and in a ring shape. The wave propagation in the medium is described by the wave equation $\dfrac{d^2 u}{dt^2} - v^2 \dfrac{d^2 u}{dx^2}=0$, with $...
10 votes
3 answers
361 views

Can't solve with NDSolve a simple circuit with a lossless transmission line (a wave equation)

My question Consider the following circuit. A lossless long transmission lines ($R' = G' = 0 \text{ } \Omega$), of length $\ell$ and inductance per unit length $L'$ and capacitance per unit length $C'$...
0 votes
0 answers
165 views

Why is regioncentroid not giving correct results?

I am trying to calculate and plot the x-axis of a volume centroid for the region between zx-plane and a function squared $u(t,x,z)$ from time $t=15$ to $25$. The function is a numerical solution to a ...
4 votes
1 answer
467 views

Solving a damped wave equation

I am trying to solve the equation $$ \frac{d^2u}{dt^2}-\frac{d^2}{dx^2}\left(c_s^2u+\nu\frac{du}{dt}\right)=0 $$ with initial conditions $$u(x, 0)=0$$ $$\frac{du}{dt}|_{t=0}=0$$ and boundary ...
2 votes
2 answers
212 views

Heat and wave equation [closed]

I have to solve the heat equation $\qquad u_t=u_{xx}+0.5 u, 0<x<1,t>0$ and $\qquad u_x (0,t)=u_x (1,t)=0, u(x,0)=[\cos(\pi x)]^2.$ I used ...