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4. Romberg integration is used to approximate f(x) dx. Find f(2.5) if f(2) find R1,1. 0.5134, f(3) = 0.3679, R31 = 0.4368 and R33 = 0.4366. Use Trapezoidal rule to c0.2 c0.6 5. Evaluate using Simpson's rule in both directions: ey- dy dx. 6. Consider the initial valye problem dy = -5y + 5t2 + 2t, 0

4. Romberg integration is used to approximate f(x) dx. Find f(2.5) if f(2) find R1,1. 0.5134, f(3) = 0.3679, R31 = 0.4368 and R33 = 0.4366. Use Trapezoidal rule to c0.2 c0.6 5. Evaluate using Simpson's rule in both directions: ey- dy dx. 6. Consider the initial valye problem dy = -5y + 5t2 + 2t, 0

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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4. Romberg integration is used to approximate f(x) dx. Find f(2.5) if f(2) find R1,1. 0.5134, f(3) = 0.3679, R31 = 0.4368 and R33 = 0.4366. Use Trapezoidal rule to c0.2 c0.6 5. Evaluate using Simpson's rule in both directions: ey-T dy dx. 6. Consider the initial valye problem dy = -5y + 5t2 + 2t, 0<t<1, y(0) = 1 dt that has exact solution y(t) = t² + e¬5t. (a) With h = 0.1, approximate y(0.2) using the Midpoint method h Yi+1 = Yi + hf|t; + Yi +f(ti, Yi) i = 0, 1, ...
Transcribed Image Text:4. Romberg integration is used to approximate f(x) dx. Find f(2.5) if f(2) find R1,1. 0.5134, f(3) = 0.3679, R31 = 0.4368 and R33 = 0.4366. Use Trapezoidal rule to c0.2 c0.6 5. Evaluate using Simpson's rule in both directions: ey-T dy dx. 6. Consider the initial valye problem dy = -5y + 5t2 + 2t, 0<t<1, y(0) = 1 dt that has exact solution y(t) = t² + e¬5t. (a) With h = 0.1, approximate y(0.2) using the Midpoint method h Yi+1 = Yi + hf|t; + Yi +f(ti, Yi) i = 0, 1, ...
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