I don't understand what other type of solution is there to render on a gpu other than a numeric one?
Here is a very basic shader for what you want:
float freq1 = 2.0;
float freq2 = 3.0;
float amp = 0.5;
pos.z += sin(pos.x * freq1 + uTime) * amp;
pos.z += cos(pos.y * freq2 + uTime) * amp;
gl_Position = projectionMatrix * modelViewMatrix * vec4(pos, 1.0);
