Solve the differential equation below under the following initial conditions: y(0.5), y(1.0) y' = sin(x) + e-x, 0 ≤ x ≤ 1, y(0) = 1 ii) Solve the differential equation in i) above numerically using a step size h = 0.5 using the various schemes:
Solve the differential equation below under the following initial conditions: y(0.5), y(1.0) y' = sin(x) + e-x, 0 ≤ x ≤ 1, y(0) = 1 ii) Solve the differential equation in i) above numerically using a step size h = 0.5 using the various schemes:
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 10CR
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i. Solve the differential equation below under the following initial conditions:
y(0.5), y(1.0)
y' = sin(x) + e-x, 0 ≤ x ≤ 1, y(0) = 1
ii) Solve the differential equation in i) above numerically using a step size h = 0.5 using the various schemes:
a. the Euler Method.
b. the Taylor Series Method of order two.
c. the second order Runge-Kutta Method.
iii) Compare the approximate solutions for y(0.5), y(1.0) using Euler's method with the exact solutions by tabulating the values and finding the corresponding absolute errors for the initial value problem.
y' = sin(x) + e-x, 0 ≤ x ≤ 1, y(0) = 1
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