User talk:Egm4313.s12.team8.tclamb/R6-2

=R6.5 Plots=

Excitation shoots off after radius of convergence.



Behavior of excitation with added perturbation of 0.01.

Behavior of excitation with added perturbation of 0.01. We note the addition of a positive perturbation decreases the accuracy of the perturbed solution.

Behavior of excitation with added perturbation of -0.01.

Behavior of excitation with added perturbation of -0.01. we note the addition of a negative perturbation increases the accuracy of the perturbed solution.

Behavior of excitation with added perturbation of -0.035.

Behavior of excitation with added perturbation of -0.035. Here we experimented with small perturbations until -0.035 brought the perturbed solution very close to the exact solution over the interval.

=R6.5 Equations= [y11p, d, c1, c2, c] = coeffsa(11, x, 0.01); d = 0  1.010000000000000  -0.490000000000000   0.343333333333333  -0.240000000000000   0.210000000000000  -0.156666666666667   0.152857142857143  -0.115000000000000   0.121111111111111  -0.090000000000000   0.100909090909091 c = 1.0e+006 * 0.000000050454545  0.000000787500000   0.000009098055556   0.000087328750000   0.000720491428571   0.005119876666667   0.030948675000000   0.155316792500000   0.622414176666667   1.868962795000001   3.739646360000001   3.740506745000001 c1 = -3.741362201271275e+006 c2 = 8.546807658191294e+002

[y11p, d, c1, c2, c] = coeffsa(11, x, -0.01); d = 0  0.990000000000000  -0.510000000000000   0.323333333333333  -0.260000000000000   0.190000000000000  -0.176666666666667   0.132857142857143  -0.135000000000000   0.101111111111111  -0.110000000000000   0.080909090909091 c1 = -2.862267947552182e+006 c2 = 6.151088875157343e+002 c = 1.0e+006 * 0.000000040454545  0.000000612500000   0.000007013055556   0.000067046250000   0.000552151428571   0.003920206666667   0.023686775000000   0.118847582500000   0.476217906666666   1.429894829999999   2.861031264999998   2.861652067499998

[y11p, d, c1, c2, c] = coeffsa(11, x, -0.035);

d = 0  0.965000000000000  -0.535000000000000   0.298333333333333  -0.285000000000000   0.165000000000000  -0.201666666666667   0.107857142857143  -0.160000000000000   0.076111111111111  -0.135000000000000   0.055909090909091 c1 = -1.763400130403329e+006 c2 = 3.156440396443165e+002 c = 1.0e+006 * 0.000000027954545  0.000000393750000   0.000004406805556   0.000041693125000   0.000341726428571   0.002420619166667   0.014609400000000   0.073261070000000   0.293472569166667   0.881059873750000   1.762762396250001   1.763083720625001

=R6.4 Code=

=R6.4 Plots=







































=R6.4 Equations=
 * $$\begin{array}{rl}

y_2(x) = y_1(x) \approx & 1.30381 e^{1 x}-0.682487 e^{2 x} +0.25 \\ & + 0.038936 \sin (1.5708 x)+0.128673 \cos (1.5708 x) \end{array}$$


 * $$\begin{array}{rl}

y_4(x) \approx & 1.29577 e^{1. x} - 0.682847 e^{2. x} + 0.25 \\ & + 0.00705066 \sin (1.1781 -4.71239 x)+0.00493286 \cos (1.1781 -4.71239 x) \\ & + 0.038936 \sin (1.5708 x)+0.128673 \cos (1.5708 x) \end{array}$$


 * $$\begin{array}{rl}

y_8(x) \approx &1.31162 e^{1 x}-0.700209 e^{2 x} + 0.25 \\ &+0.0000985159 \sin (9.03208 -36.1283 x) \sin (6.28319 -25.1327 x) \\ &+0.000364302 \sin (8.24668 -32.9867 x) \sin (6.28319 -25.1327 x) \\ &+0.00246643 \sin (7.46128 -29.8451 x) \sin (6.28319 -25.1327 x) \\ &+0.0668894 \sin (6.67588 -26.7035 x) \sin (6.28319 -25.1327 x) \\ &+0.0668894 \sin (6.28319 -25.1327 x) \sin (5.89049 -23.5619 x) \\ &+0.00246643 \sin (6.28319 -25.1327 x) \sin (5.10509 -20.4204 x) \\ &+0.000364302 \sin (6.28319 -25.1327 x) \sin (4.31969 -17.2788 x) \\ &+0.0000985159 \sin (6.28319 -25.1327 x) \sin (3.53429 -14.1372 x) \\ &+0.0000985159 \cos (9.03208 -36.1283 x) \cos (6.28319 -25.1327 x) \\ &+0.000364302 \cos (8.24668 -32.9867 x) \cos (6.28319 -25.1327 x) \\ &+0.00246643 \cos (7.46128 -29.8451 x) \cos (6.28319 -25.1327 x) \\ &+0.0668894 \cos (6.67588 -26.7035 x) \cos (6.28319 -25.1327 x) \\ &+0.0668894 \cos (5.89049 -23.5619 x) \cos (6.28319 -25.1327 x) \\ &+0.00246643 \cos (5.10509 -20.4204 x) \cos (6.28319 -25.1327 x) \\ &+0.000364302 \cos (4.31969 -17.2788 x) \cos (6.28319 -25.1327 x) \\ &+0.0000985159 \cos (3.53429 -14.1372 x) \cos (6.28319 -25.1327 x) \\ &+0.000355107 \sin (9.03208 -36.1283 x) \cos (6.28319 -25.1327 x) \\ &+0.000922816 \sin (8.24668 -32.9867 x) \cos (6.28319 -25.1327 x) \\ &+0.00352533 \sin (7.46128 -29.8451 x) \cos (6.28319 -25.1327 x) \\ &+0.00663447 \sin (6.67588 -26.7035 x) \cos (6.28319 -25.1327 x) \\ &-0.00663447 \sin (5.89049 -23.5619 x) \cos (6.28319 -25.1327 x) \\ &-0.00352533 \sin (5.10509 -20.4204 x) \cos (6.28319 -25.1327 x) \\ &-0.000922816 \sin (4.31969 -17.2788 x) \cos (6.28319 -25.1327 x) \\ &-0.000355107 \sin (3.53429 -14.1372 x) \cos (6.28319 -25.1327 x) \\ &-0.000355107 \sin (6.28319 -25.1327 x) \cos (9.03208 -36.1283 x) \\ &-0.000922816 \sin (6.28319 -25.1327 x) \cos (8.24668 -32.9867 x) \\ &-0.00352533 \sin (6.28319 -25.1327 x) \cos (7.46128 -29.8451 x) \\ &-0.00663447 \sin (6.28319 -25.1327 x) \cos (6.67588 -26.7035 x) \\ &+0.00663447 \sin (6.28319 -25.1327 x) \cos (5.89049 -23.5619 x) \\ &+0.00352533 \sin (6.28319 -25.1327 x) \cos (5.10509 -20.4204 x) \\ &+0.000922816 \sin (6.28319 -25.1327 x) \cos (4.31969 -17.2788 x) \\ &+0.000355107 \sin (6.28319 -25.1327 x) \cos (3.53429 -14.1372 x) \\ \end{array}$$

=R6.2 Images=