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where σ,r,bER are parameters. Set σ = 10, r = 28 and b = 8/3. dx = σ(y-x), dt WW dy =rx-y-xz, dt ## dz = xy-bz, dt (a) Plot x(t) with initial data x(0) = y(0) = z(0) = 5. Also plot x(t) with initial data x(0) = 5.01, y(0) = z(0) = 5. (b) Plot the projections in the xy- and xz-planes of the solution with initial data x(0) = y(0) = z(0) = 5. Now set σ 10 and b = 8/3. (c) For each of the four values of r = 100.9125, 100.915, 100.9175 and 100.92, plot the projection in the xz-plane of the solution with initial data x(0) = -5, y(0) = -13, z(0) = 55.

where σ,r,bER are parameters. Set σ = 10, r = 28 and b = 8/3. dx = σ(y-x), dt WW dy =rx-y-xz, dt ## dz = xy-bz, dt (a) Plot x(t) with initial data x(0) = y(0) = z(0) = 5. Also plot x(t) with initial data x(0) = 5.01, y(0) = z(0) = 5. (b) Plot the projections in the xy- and xz-planes of the solution with initial data x(0) = y(0) = z(0) = 5. Now set σ 10 and b = 8/3. (c) For each of the four values of r = 100.9125, 100.915, 100.9175 and 100.92, plot the projection in the xz-plane of the solution with initial data x(0) = -5, y(0) = -13, z(0) = 55.

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 using a Runge-Kutta solver to compute numerical solutions in 0 ≤ t ≤ 50 of the Lorenz equations

where σ,r,bER are parameters. Set σ = 10, r = 28 and b = 8/3. dx = σ(y-x), dt WW dy =rx-y-xz, dt ## dz = xy-bz, dt (a) Plot x(t) with initial data x(0) = y(0) = z(0) = 5. Also plot x(t) with initial data x(0) = 5.01, y(0) = z(0) = 5. (b) Plot the projections in the xy- and xz-planes of the solution with initial data x(0) = y(0) = z(0) = 5. Now set σ 10 and b = 8/3. (c) For each of the four values of r = 100.9125, 100.915, 100.9175 and 100.92, plot the projection in the xz-plane of the solution with initial data x(0) = -5, y(0) = -13, z(0) = 55.
Transcribed Image Text:where σ,r,bER are parameters. Set σ = 10, r = 28 and b = 8/3. dx = σ(y-x), dt WW dy =rx-y-xz, dt ## dz = xy-bz, dt (a) Plot x(t) with initial data x(0) = y(0) = z(0) = 5. Also plot x(t) with initial data x(0) = 5.01, y(0) = z(0) = 5. (b) Plot the projections in the xy- and xz-planes of the solution with initial data x(0) = y(0) = z(0) = 5. Now set σ 10 and b = 8/3. (c) For each of the four values of r = 100.9125, 100.915, 100.9175 and 100.92, plot the projection in the xz-plane of the solution with initial data x(0) = -5, y(0) = -13, z(0) = 55.
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