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Consider the following first-order ODE: dy 4e0.8x – 0.5y, x = [0, 1], y(x = 0) = 2 %3D dx The analytical solution of this equation is determined, as follows: 4 (e0.8x – e-0.5x) + 2e 1.3 -0.5x У (х) - Using step size h = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decin %3D places) Yi Yi Yi (Analytical, Xi (Predictor, (Corrector, from Error Euler's) Heun's) analytical solution) 0. 0. 1 0.25 0.50 3 0.75 4. 1.00

Consider the following first-order ODE: dy 4e0.8x – 0.5y, x = [0, 1], y(x = 0) = 2 %3D dx The analytical solution of this equation is determined, as follows: 4 (e0.8x – e-0.5x) + 2e 1.3 -0.5x У (х) - Using step size h = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decin %3D places) Yi Yi Yi (Analytical, Xi (Predictor, (Corrector, from Error Euler's) Heun's) analytical solution) 0. 0. 1 0.25 0.50 3 0.75 4. 1.00

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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Consider the following first-order ODE: dy 4e0.8x – 0.5y, dx x = [0, 1], y(x = 0) = 2 The analytical solution of this equation is determined, as follows: 4 y (x) = (e0.8x – e-0.5x) + 2e¬0.5x 1.3 Using step sizeh = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decimal places) %3D Yi Yi Yi (Analytical, (Predictor, (Corrector, from Error Euler's) Heun's). analytical solution) 1 0.25 2 0.50 3 0.75 4 1.00
Transcribed Image Text:Consider the following first-order ODE: dy 4e0.8x – 0.5y, dx x = [0, 1], y(x = 0) = 2 The analytical solution of this equation is determined, as follows: 4 y (x) = (e0.8x – e-0.5x) + 2e¬0.5x 1.3 Using step sizeh = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decimal places) %3D Yi Yi Yi (Analytical, (Predictor, (Corrector, from Error Euler's) Heun's). analytical solution) 1 0.25 2 0.50 3 0.75 4 1.00
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