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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!

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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!

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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!