# Question:How to solve coupled singular boundary value problem with midrich.

## Question:How to solve coupled singular boundary value problem with midrich.

Maple

restart; with(plots);
G := 1; M := .1; R := 1; P := .72; alpha := .1; phi := 1; K := 1; n := 2; beta := 1;
1
0.1
1
0.72
0.1
1
1
2
1
ode1 := {(1+(4/3)*R)*(diff(theta(x), x, x))+(1/2)*P*f(x)*(diff(theta(x), x))+alpha*theta(x) = 0, n*(diff(f(x), x, x))^(n-1)*(diff(f(x), x, x, x))+f(x)*(diff(f(x), x, x))/(n+1)+G*theta(x)-M*(diff(f(x), x)) = 0, f(0) = 0, theta(10) = 0, (D(f))(0) = beta*K*((D@@2)(f))(0), (D(f))(10) = 1, (D(theta))(0) = -phi*(1-theta(0))};
/7  d  / d          \                     / d          \
{ - --- |--- theta(x)| + 0.3600000000 f(x) |--- theta(x)|
\3  dx \ dx         /                     \ dx         /

/ d  / d      \\ / d  / d  / d      \\\
+ 0.1 theta(x) = 0, 2 |--- |--- f(x)|| |--- |--- |--- f(x)|||
\ dx \ dx     // \ dx \ dx \ dx     ///

1      / d  / d      \\                  / d      \
+ - f(x) |--- |--- f(x)|| + theta(x) - 0.1 |--- f(x)| = 0,
3      \ dx \ dx     //                  \ dx     /

f(0) = 0, theta(10) = 0, D(f)(0) = @@(D, 2)(f)(0),

\
D(f)(10) = 1, D(theta)(0) = -1 + theta(0) }
/
dsol := dsolve(ode1, numeric, method = bvp[midrich], range = 0 .. 10);
Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

﻿