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Given the IVP dy =x² – sin y, y(0)=.5 dx Estimate y(0.4) using 4th order RK method with step size h=0.2.

Given the IVP dy =x² – sin y, y(0)=.5 dx Estimate y(0.4) using 4th order RK method with step size h=0.2.

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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Given the IVP ay – x² – sin y, y(0) =.5 dx Estimate y(0.4) using 4th order RK method with step size h=0.2. For a chemical reaction, the rate of change of the concentration of component A is described by the differential equation: dCa - -k,Ca - k,C, dt Where CA concentration of A (moles/liter) ki rate constant = 2.7 hr k2 rate constant = 0.8 hr-' (moles/liter)1 The initial concentration of A is: CA (0) = 3.0 mole/liter Determine the concentration of A at t = 1/4 hr, 1/2 hr, using the fourth order Runge-Kutta method, with h = 1/4 hr.
Transcribed Image Text:Given the IVP ay – x² – sin y, y(0) =.5 dx Estimate y(0.4) using 4th order RK method with step size h=0.2. For a chemical reaction, the rate of change of the concentration of component A is described by the differential equation: dCa - -k,Ca - k,C, dt Where CA concentration of A (moles/liter) ki rate constant = 2.7 hr k2 rate constant = 0.8 hr-' (moles/liter)1 The initial concentration of A is: CA (0) = 3.0 mole/liter Determine the concentration of A at t = 1/4 hr, 1/2 hr, using the fourth order Runge-Kutta method, with h = 1/4 hr.
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