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How to solve a boundary value problem (differential equations) which contains dependent variable values at the boundary??? The equation is like a integro-differential equation.

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T S Singh
T S Singh 2017-4-11
评论： T S Singh 2017-4-12
(-iy+y'''')=(A+Bx)y'''(0)+(C+Dx)y''(0)
  1. Here A,B,C and D are constants.
  2. y'''(0) are the dependent variable 3rd order derivative at x=0.
  3. Like wise y''(0) is the 2nd oder derivative of y at x=0
  4. BCs y(0)=0, y'(0)=1, y''(1)=0 and y'''(1)=0

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Torsten
Torsten 2017-4-12
编辑：Torsten 2017-4-12
Try "dsolve" on the problem
(-iy+y'''')=(A+Bx)*C2+(C+Dx)*C1
with boundary conditions
y(0)=0, y'(0)=1, y''(1)=0, y'''(1)=0, y''(0)=C1, y'''(0)=C2.
Best wishes
Torsten.
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Torsten
Torsten 2017-4-12
Since there is no integral involved in the differential equation, I don't see an obvious relation to integro-differential equations. But I might be wrong.
Best wishes
Torsten.
T S Singh
T S Singh 2017-4-12
Sorry I forgot to mention, the y'''(0) and y''(0) term in the differential equation was obtained from an integration expression, and these two terms remained because y'''(1) and y''(1) are zero because of the boundary conditions.

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