a- Use Euler’s method to integrate dy/dt = y − t^2 + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5. b- Employ the classical fourth-order Runge-Kutta (RK) method to integrate dy/dt= y − t^2 + 1 from t=0 to 0.2 with a step size of 0.05. The initial condition at t=0 is y=0.5. c- Compare the true percent relative error values ( |Et|%) Note that the exact ( analytical) solution was given in the tables.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.