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The second-order Adams-Bashforth method for the integration of a single first-order differential equation d.x =f(t, x) dt is Xn+1 = X₁ + 1 h[3f(t, Xn) – f(tn-1, Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx == f₁(t, x, y), dy= dy = f(t, x, y) dt dt Hence find the value of X(0.3) for the initial-value problem d²x dx + x = sint, x(0) = 0, dx (0) = 1 dt² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.

The second-order Adams-Bashforth method for the integration of a single first-order differential equation d.x =f(t, x) dt is Xn+1 = X₁ + 1 h[3f(t, Xn) – f(tn-1, Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx == f₁(t, x, y), dy= dy = f(t, x, y) dt dt Hence find the value of X(0.3) for the initial-value problem d²x dx + x = sint, x(0) = 0, dx (0) = 1 dt² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.

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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2.4.3 The second-order Adams-Bashforth method for the integration of a single first-order differential equation dx == f(t, x) dt is Xn+1 = X₂ + 1 h[3f(tns Xn) − ƒ(tn-19 Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx = f₁(t, x, y), d=f₂(t, x, y) dt Hence find the value of X(0.3) for the initial-value problem d²x 2 dx +x= sint, x(0)=0, dx (0) = 1 - di² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.
Transcribed Image Text:2.4.3 The second-order Adams-Bashforth method for the integration of a single first-order differential equation dx == f(t, x) dt is Xn+1 = X₂ + 1 h[3f(tns Xn) − ƒ(tn-19 Xn-1)] Write down the appropriate equations for applying the same method to the solution of the pair of differential equations dx = f₁(t, x, y), d=f₂(t, x, y) dt Hence find the value of X(0.3) for the initial-value problem d²x 2 dx +x= sint, x(0)=0, dx (0) = 1 - di² dt dt using this Adams-Bashforth method with step size h = 0.1. Use the second-order predictor-corrector method for the first step to start the computation.
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