3 added 3 characters in body

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t]
-xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;

\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t)
f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];

c = 1/2;

NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

t/(1 - t) == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 -
q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t] -xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;
\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t) f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];
c = 1/2;
NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

t/(1 - t) == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 - q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t]
-xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;

\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t)
f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];

c = 1/2;

NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

t/(1 - t) == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 -
q)/q}, f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

2 deleted 4 characters in body

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t] -xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;
\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t) f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];
c = 1/2;
NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

(t/(1 - t))^2 == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 - q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t] -xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;
\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t) f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];
c = 1/2;
NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

(t/(1 - t))^2 == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 - q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t] -xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;
\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t) f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];
c = 1/2;
NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

t/(1 - t) == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 - q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!

1

# Solving Differential Equation for derivative

I am new to mathematica and am trying to solve a differential equation. Actually, I am not entirely sure if the system can be called differential equation.

I am interested in finding out the second derivative of the system. The actual function and the first derivative only enter the system at local points, i.e. 1/2, 1, and a constant t which should be uniquely determined by the system.

I have tried Dsolve first but I guess the system is to complicated to get an analytical solution, so a numerical one would be nice to have too.

My code is:

\[Sigma]A = 1/2 + (1 - t) f'[1] - f[1] + f[t] - (t - 1/2) xbB'[t] + xbB[t] -xbB[1/2] + 1/2 xaB'[1] - xaB[1] + xaB[1/2] - xaB'[1] + xaB'[1/2] ;
\[Sigma]B = 1/2 - 1/2 xaB'[1] + xaB[1] - xaB[1/2] + f'[1] - f'[1/2] - (1-t) f'[1] + f[1] - f[t] + (t - 1/2) xbB'[t] - xbB[t] + xbB[1/2];
c = 1/2;
NDSolve[
{
f''[t] == 0,
xaB''[1] == c,
f''[q] == - xbB''[q],

f'[t] == 0,
xbB'[1/2] == 0,
xaB'[1/2] == 0,

(t/(1 - t))^2 == \[Sigma]A / \[Sigma]B,

((c - f''[q] )/(c + f''[q]))^2 == ((1 - q)/q)^2 *\[Sigma]A/\[Sigma]B,
(c - f''[q] )/(c + f''[q]) *(c - xaB''[q])/(c + xaB''[q] )  q/(1-q) == (1 - q)/q},

f''[q], {q, 1/2, 1}]


I have only included the conditions on the functions that I really need for the solution of f'' to be correct. However, I have tried different combinations of starting conditions. As I am only interested in the second derivatives, the constants in the other 2 functions can be chosen freely. or to solve the system for f or f' instead of f'' (I'm not even sure if NDSolve does solve for the derivatives directly?)

As I said I'm new to mathematica and this Forum so if there is any further info I should supply or format I should use, just let me know. I have searched for related questions during hours but none seemed to apply to my problem.

Thank you in advance for any assistance!