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a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 1/12) 2' h k₂ k3= hfti + , Wi + 2 2 k4 = hf (ti+h, wi + k3), Wi+1 = wi + (k₁ + 2k2 + 2k3 + ka), when applied to the differential equation y' = Ay, can be written in the form 1 Wi+1 ₁ = (1 + hλ + 1/ (hx)² + 1 (hx)³ + 2/7 (hd)*) wr. 24

a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 1/12) 2' h k₂ k3= hfti + , Wi + 2 2 k4 = hf (ti+h, wi + k3), Wi+1 = wi + (k₁ + 2k2 + 2k3 + ka), when applied to the differential equation y' = Ay, can be written in the form 1 Wi+1 ₁ = (1 + hλ + 1/ (hx)² + 1 (hx)³ + 2/7 (hd)*) wr. 24

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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a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 2 2 h k3 = hfti + Wi + 2¹ 2 k4 = hf (ti + h, wi + k3), 1 W₁+1 =W₁ + (k₁ + 2k2 + 2k3+k4), when applied to the differential equation y' = Ay, can be written in the form 1 Wi+1 = = (1 + hλ + 1 (hx)² + = (ha)³ + 2/7 (hX)^) wi- Wi. 24
Transcribed Image Text:a) Show that the fourth-order Runge-Kutta method, k₁ = hf (ti, wi), h k₁ k₂= hfti+ Wi + 2 2 h k3 = hfti + Wi + 2¹ 2 k4 = hf (ti + h, wi + k3), 1 W₁+1 =W₁ + (k₁ + 2k2 + 2k3+k4), when applied to the differential equation y' = Ay, can be written in the form 1 Wi+1 = = (1 + hλ + 1 (hx)² + = (ha)³ + 2/7 (hX)^) wi- Wi. 24
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