Computationally Efficient Technique for Solving ODE Systems Exhibiting Initial and Boundary Layers

Figure 1

Red (dashed): 𝑥 (direct numerical solution of (1.1)), Green (dashed-dotted): 𝑥⁽¹⁾ (solution of (5.3) using (5.4)), Blue (solid): 𝑥⁽²⁾ (solution of (5.3) using (5.5)), Black (dotted): 𝑥⁽⁰⁾ (standard first-order solution (5.2)).