We have developed a (new) numerical scheme to solve the classical wave equation in 3 dimensions and we aim to publish the results.
We can read in the aim and scope of the journal of computational and applied mathematics :
" ...The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples"
Immediately we can raise the question : What are known (or classical) nontrivial examples of exact solutions of the 3D wave equation? by that I mean the Cauchy problem : $$u_{tt}=c^2\Delta u,\quad u(X,0)= f(X),\quad u_t(X,0)= g(X)$$ Nontrivial examples against which we can compare the results of the numerical scheme, that is, we need given $f$ and $g$, along with a 'computable' formula for $u(X,t)= u(x,y,z,t)$