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4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [O, ½], first with step size h 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = with the value y(%) of the actual solution. y' = (1 + y²),y(0) = 1; y(x) = tan (x+1) approx. "exact" Xn f(xn Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 1 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 0.3 0.1 0.4 1.223049 0.4 0.1 0.5 1.287427 3. 4-

4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [O, ½], first with step size h 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = with the value y(%) of the actual solution. y' = (1 + y²),y(0) = 1; y(x) = tan (x+1) approx. "exact" Xn f(xn Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 1 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 0.3 0.1 0.4 1.223049 0.4 0.1 0.5 1.287427 3. 4-

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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4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [0, ½], first with step size h = 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = h with the value y(%) of the actual solution. y' = (1 + y?), y(0) = 1; y(x) = tan (x +1) %3D approx. "ехact" Xn f(xn, Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 0 0 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 3 0.3 0.1 0.4 1.223049 4 0.4 0.1 0.5 1.287427
Transcribed Image Text:4. An initial value problem and its exact solution y(x) are given below. Apply Euler's method twice to approximate to this solution on the interval [0, ½], first with step size h = 0.25 (two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-place values of the two approximations at x = h with the value y(%) of the actual solution. y' = (1 + y?), y(0) = 1; y(x) = tan (x +1) %3D approx. "ехact" Xn f(xn, Yn) h f(xn Yn) Yn Yn+1 Xn+1 Yn+1 1 0.25 0.25 1.133519 1 0.25 0.25 0.5 1.287427 0 0 0.1 0.1 1.051293 1 00.1 0.1 0.2 1.105356 0.2 0.1 0.3 1.162492 3 0.3 0.1 0.4 1.223049 4 0.4 0.1 0.5 1.287427
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