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1. Perform three iterations of the fourth-order Runge-Kutta method for the following syster of equations: (a) (b) u₁=3u₁ +2u₂ (2t² + 1) e²t u₂ = 4₁+ ₂+ (t² + 2t-4) et with u₁ (0) = u2(0) = 1 and h = 0.2 = -4u₁-2u₂+ cost + 4 sint 3u1 + u2-3 sint u₂ = with u₁(0) = 0, u2(0) = -1 and h = 0.1 u₁ U2 (c) ₂ = -₁ -2e +1 uz = -u₁-e²+1 with u₁(0)=u3(0) = 1, u₂(0) = 0 and h = 0.5 = U₂-U3+t 31² u₂+e-t with u₁ (0) = u2(0) = 1, u3(0) = (d) u h = 0.1

1. Perform three iterations of the fourth-order Runge-Kutta method for the following syster of equations: (a) (b) u₁=3u₁ +2u₂ (2t² + 1) e²t u₂ = 4₁+ ₂+ (t² + 2t-4) et with u₁ (0) = u2(0) = 1 and h = 0.2 = -4u₁-2u₂+ cost + 4 sint 3u1 + u2-3 sint u₂ = with u₁(0) = 0, u2(0) = -1 and h = 0.1 u₁ U2 (c) ₂ = -₁ -2e +1 uz = -u₁-e²+1 with u₁(0)=u3(0) = 1, u₂(0) = 0 and h = 0.5 = U₂-U3+t 31² u₂+e-t with u₁ (0) = u2(0) = 1, u3(0) = (d) u h = 0.1

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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1. Perform three iterations of the fourth-order Runge-Kutta method for the following syster of equations: (a) (b) u₁=3u₁ +2₂ - (2t² + 1) e²t u₂ = 4₁+U₂ + (t² + 2t - 4) et with u₁(0) = u2(0) = 1 and h = 0.2 u₁ = -4u₁-2u₂+ cost + 4 sint 3u1 + U2 -3 sint u₂ = with u₁(0) = 0, u₂(0) = -1 and h = 0.1 u₁ U2 (c) ₂ = -u₁-2e²+1 uz = -u₁-e²+1 with u₁(0)=1 uz (0) = 1, u₂(0) = 0 and h = 0.5 u₁ U₂ -Uz+t 31² uz U₂ + e-t with u₁(0) = u2(0) (d) u = = 1, u3(0) h = 0.1
Transcribed Image Text:1. Perform three iterations of the fourth-order Runge-Kutta method for the following syster of equations: (a) (b) u₁=3u₁ +2₂ - (2t² + 1) e²t u₂ = 4₁+U₂ + (t² + 2t - 4) et with u₁(0) = u2(0) = 1 and h = 0.2 u₁ = -4u₁-2u₂+ cost + 4 sint 3u1 + U2 -3 sint u₂ = with u₁(0) = 0, u₂(0) = -1 and h = 0.1 u₁ U2 (c) ₂ = -u₁-2e²+1 uz = -u₁-e²+1 with u₁(0)=1 uz (0) = 1, u₂(0) = 0 and h = 0.5 u₁ U₂ -Uz+t 31² uz U₂ + e-t with u₁(0) = u2(0) (d) u = = 1, u3(0) h = 0.1
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