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Consider the IVP Jy = −y+t+1, y(0) = 1 Compute the local truncation error for the Euler method using ť” = ln(4)and h = ln(2). The local truncation error is defined as Sn = [y(tn) + hf(t¹, y(tn))] − y(tn+¹) Hint: The solution of a linear 1st order ODE, y' + p(t)y = g(t) is of the form y(t) (Sμ(t)g(t)dt+C) with µ(t) = el p(t)dt μ(t) The constant C is determined from the initial value. For this question the exact solution is y(t) =t+e-t. O(-In 3) O(-In 3) ○(-In 2) (-In 2)

Consider the IVP Jy = −y+t+1, y(0) = 1 Compute the local truncation error for the Euler method using ť” = ln(4)and h = ln(2). The local truncation error is defined as Sn = [y(tn) + hf(t¹, y(tn))] − y(tn+¹) Hint: The solution of a linear 1st order ODE, y' + p(t)y = g(t) is of the form y(t) (Sμ(t)g(t)dt+C) with µ(t) = el p(t)dt μ(t) The constant C is determined from the initial value. For this question the exact solution is y(t) =t+e-t. O(-In 3) O(-In 3) ○(-In 2) (-In 2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the IVP Jy = −y+t+1, y(0) = 1 Compute the local truncation error for the Euler method using ť” = ln(4)and h = ln(2). The local truncation error is defined as Sn = [y(tn) + hf(t¹, y(tn))] − y(tn+¹) Hint: The solution of a linear 1st order ODE, y' + p(t)y = g(t) is of the form y(t) (Sμ(t)g(t)dt+C) with µ(t) = el p(t)dt μ(t) The constant C is determined from the initial value. For this question the exact solution is y(t) =t+e-t. O(-In 3) O(-In 3) ○(-In 2) (-In 2)
Transcribed Image Text:Consider the IVP Jy = −y+t+1, y(0) = 1 Compute the local truncation error for the Euler method using ť” = ln(4)and h = ln(2). The local truncation error is defined as Sn = [y(tn) + hf(t¹, y(tn))] − y(tn+¹) Hint: The solution of a linear 1st order ODE, y' + p(t)y = g(t) is of the form y(t) (Sμ(t)g(t)dt+C) with µ(t) = el p(t)dt μ(t) The constant C is determined from the initial value. For this question the exact solution is y(t) =t+e-t. O(-In 3) O(-In 3) ○(-In 2) (-In 2)
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