Question

Let x˙=−3x+5,x0=2, h=0.1, use the

(a) Forward Euler,
(b) Back Euler, and
(c) Trap methods respectively to compute the solution for two steps.

Answer 1

To compute the solution for two steps using the Forward Euler, Back Euler, and Trapezoidal methods, we can use the respective formulas to update the value of x. By substituting the given values, we can calculate the solutions step by step.

Step-by-step explanation:

To compute the solution for two steps using the Forward Euler method, we can use the formula:

xn+1 = xn + h * f(xn)

where xn is the previous value of x, h is the step size, and f(xn) is the derivative of x with respect to t evaluated at xn.

Using this formula, we can calculate x1 and x2 by substituting the given values.

Similarly, for the Back Euler method, we use the formula:

xn+1 = xn + h * f(xn+1)

And for the Trapezoidal method, we use the formula:

xn+1 = xn + h/2 * (f(xn) + f(xn+1))

Following these steps, we can compute the solutions for two steps using the Forward Euler, Back Euler, and Trapezoidal methods.