odes_euler

odes_euler, considers the approximate solution of an ordinary differential equation (ODE) using Euler's method.

The notes:

• odes_euler.pdf
• odes_euler.tex

Scripts and functions:

• euler.m, accepts values of yprime, n, a, b, y0, and uses Euler's method to approximate the solution from a to b, using n steps, initial condition y0, and the derivative function yprime(t,y).
• expo_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• expo_exact.m, the exact solution to the exponential test problem for given values of t and y0.
• expo_prime.m, the right hand side of the exponential test problem.
• negexp_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• negexp_exact.m, the exact solution to the negative exponential test problem.
• negexp_prime.m, the right hand side of the negative exponential test problem.
• pendulum_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• pendulum_exact.m, the exact solution to the pendulum test problem.
• pendulum_prime.m, the right hand side of the pendulum test problem.
• pendulum_nonlinear_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• pendulum_nonlinear_prime.m, the right hand side of the nonlinear pendulum test problem.
• quadratic_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• quadratic_exact.m, returns the exact solution to the quadratic test problem for given values of t and y0.
• quadratic_euler_error.m, looks at the error in Euler's method to the quadratic test problem.
• quadratic_prime.m, the right hand side of the quadratic test problem.

Images:

• expo.png, a plot of an approximate solution of the exponential test problem.
• negexp.png, a plot of an approximate solution of the negative exponential test problem.
• pendulum.png, a plot of an approximate solution of the pendulum test problem.
• pendulum_nonlinear.png, a plot of an approximate solution of the nonlinear pendulum test problem.
• quadratic.png, a plot comparing exact and approximate solutions of the quadratic test problem.
• steps.png, illustrates how a continuous ODE is approximated by a sequence of steps.