Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

Figure 7

Snapshots of numerical solutions for (43) at 𝑡=0.3. In (a), the exact solution is 𝑢=exp(𝑥−𝑡)−exp(−𝑥+𝑡)/2 if 𝑥<0 and 𝑢=exp(−𝑥/√2−𝑡) − exp(𝑥/√2+𝑡)/2 otherwise. In (b), the exact solution is 𝑢=exp(𝑥+𝑡) − exp(−𝑥−𝑡) if 𝑥<0 and 𝑢=exp(𝑥/√2−𝑡)+exp(−𝑥/√2+𝑡) otherwise.

(a)

(b)