07-Jan-2022 16:45:16
bvp4c_test():
MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
Test bvp4c().
bratu():
Use BVP4C to solve the following boundary value problem:
y" + lambda * exp ( y ) = 0
y(0) = 0, y(1) = 0
When lambda = 1, there are two solutions.
Try
y(x) = 0.1, y'(x) = 0.
and
y(x) = 3.0, y'(x) = 0.0
Saving plot file as "bratu_0.450000.png"
Saving plot file as "bratu_1.000000.png"
Saving plot file as "bratu_3.500000.png"
bratu():
Normal end of execution.
example1():
Use BVP4C to solve the following boundary value problem:
u' = 0.5 * u * ( w - u ) / v
v' = - 0.5 * ( w - u )
w' = ( 0.9 - 1000 * ( 2 - y ) - 0.5 * w * ( w - u ) ) / z
z' = 0.5 * ( w - u )
y' = - 100 * ( y - w )
u(0) = v(0) = w(0) = 1
z(0) = - 10
w(1) - y(1) = 0.0
Use initial guesses:
u(x) = 1
v(x) = 1
w(x) = -4.5 * x^2 + 8.91 * x + 1
z(x) = -10
y(x) = - 4.5 * x^2 + 9 * x + 0.91
Saving plot file as "example1.png"
EXAMPLE1:
Normal end of execution.
example2():
Use BVP4C to solve the following boundary value problem:
y" + 3 p y / ( p + t^2 )^2 = 0
y(-0.1) = -0.1 / sqrt ( p + 0.01 )
y(+0.1) = +0.1 / sqrt ( p + 0.01 )
Use initial guesses:
y(x) = 0
y'(x) = 10
Use parameter value p = 1e-05
Saving plot file as "example2.png"
EXAMPLE2:
Normal end of execution.
example3():
Use BVP4C to solve the following eigenvalue boundary value problem:
y" + (lambda - 2 q cos(2x) y = 0
y'(0) = 0, y'(pi) = 0, y(0) 1
The initial guess is set using the functional form for y_init.
Computed eigenvalue lambda = 17.0971
Saving plot file as "example3.png"
EXAMPLE3:
Normal end of execution.
example4():
Use BVP4C to solve a boundary value problem with
a periodic solution of unknown period P.
We solve this on [0,1], with P an additional unknown.
y' = 3 ( y + z - y^3/3 - 1.3
z' = - ( y - 0.7 + 0.8 * z ) / 3
y(0) = y(P), z(0) = z(P)
Use initial guess y = sin ( 2 pi x ), z = cos ( 2 pi x ).
Initial estimate for P is 6.28319
Period P = 10.7108
Saving plot file as "example4.png"
EXAMPLE4:
Normal end of execution.
sample1():
Use BVP4C to solve the following boundary value problem:
y" + abs(y) = 0
y(0) = 0, y(4) = -2
Use initial guesses y(x) = 1, y'(x) = 0.
Saving plot file as "sample1.png"
sample1():
Normal end of execution.
bvp4c_test():
Normal end of execution.
07-Jan-2022 16:45:23