Solución de un problema de valores iniciales para un sistema hiperbólico lineal
Especifique un sistema hiperbólico lineal no homogéneo con coeficientes constantes.
In[1]:=
![Click for copyable input](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/In_44.png)
eqns = {D[u[x, t], t] == D[v[x, t], x] + 1,
D[v[x, t], t] == -D[u[x, t], x] - 1};
Establezca las condiciones iniciales para el sistema.
In[2]:=
![Click for copyable input](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/In_45.png)
ic = {u[x, 0] == Cos[x]^2, v[x, 0] == Sin[x]};
Resuelva el sistema usando DSolveValue.
In[3]:=
![Click for copyable input](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/In_46.png)
sol = DSolveValue[{eqns, ic}, {u[x, t], v[x, t]}, {x, t}] //
FullSimplify
Out[3]=
![](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/O_26.png)
Visualice la solución.
In[4]:=
![Click for copyable input](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/In_47.png)
Plot3D[sol // Evaluate, {x, 0, 4}, {t, 0, 3}, PlotRange -> {-70, 120}]
Out[4]=
![](assets.es/solve-an-initial-value-problem-for-a-linear-hyperb/O_27.png)