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