E. Kreyszig, Advanced Engineering Mathematics, Tenth Edition.

MATH 528: Fall 2015 Due: 15 Sept 2015 (in class)

Homework 4

• Numerical Methods for First-Order ODEs You are encouraged (but not required) to use a computer to assist you with this problem. Include a printout of any code you use to complete this problem.

– Consider the following IVP: y′ + 18xy2 = 0 with y(0) = 1.

1. Find the exact solution for y(x), and determine the value of y(1). 2. Using the Euler method with step size h = 0.1, find an estimate for y(1).

What is the error? 3. Using the improved Euler method with step size h = 0.1, find an estimate for

y(1). What is the error? 4. Using the Runge-Kutta Method (fourth order) with step size h = 0.1, find an

estimate for y(1). What is the error? 5. By what factor do you expect the error to be reduced for each method if the

step size is reduced from h = 0.1 to h = 0.05?

• Systems of Differential Equations

– Problem Set 4.3: #18, setup the system of differential equations for the fertilizer contents y1(t) and y2(t) but do not solve. Write the system in matrix form.

– Problem Set 4.3: #19, setup the system of differential equations for the currents I1(t) and I2(t) but do not solve. Write the system in matrix form.

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