Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

Figure 2

Numerical solutions for 𝑢_𝑡+𝑎𝑢_𝑥=sin(𝑥/𝜀): a solution 𝑢=(𝑥−𝑡)(sin(𝑥−𝑡)+2)⁻¹−𝜀cos(𝑥/𝜀) is used to generate initial/boundary conditions and measure errors.

(a) 𝜀=1

(b) 𝜀=0.01