Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

Figure 5

Time evolution of the errors in numerical solutions for 𝑢_𝑡𝑡=exp(−𝑥/𝜀)𝑢_𝑥𝑥,0≤𝑥≤1. The exact solution 𝑢=(1+𝑥)𝑡² + 𝑥𝑡+𝑥+2(−𝜀²+2𝜀³+(−𝜀+𝜀²)𝑥+(𝜀²−2𝜀³+𝜀²𝑥)exp(𝑥/𝜀)) is used to generate the initial/boundary conditions and measure the errors.

(a) 𝜀=1

(b) 𝜀=0.05