A Reliable Analytical Method for Solving Higher-Order Initial Value Problems

Figure 2

Plots of four iterates of RPS approximation for (49) and (52) when 𝑘=2,3,4,10 together with the initial guess approximation and the exact solution; blue: 𝑥_initial(𝑡); brown: 𝑥²(𝑡); green: 𝑥³(𝑡); red: 𝑥⁴(𝑡); purple: 𝑥¹⁰(𝑡); (-·-): 𝑥_exact(𝑡).