RK4 Method Code

Sarita March

2018 12 14

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I need help with the coding for MATLAB

Problem 1: Consider the following Initial Value Problem (IVP) where ? is the dependent variable and ? is the independent variable: ? ′ = sin(?) ∗ (1 − ?) with ?(0) = ?0 and ? ≥ 0 Note: the analytic solution for this IVP is: ?(?) = 1 + (?0 − 1)?^cos(?)−1

Part 1C: Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition ?0 = − 1 2 ; time step ℎ = 1 16 ; and time interval ? ∈ [0,20]

+ Plot the RK4 method approximation

+ Plot the absolute error between the approximation and the exact solution using a semilog plot