Recent content by matematikawan

  1. M

    A Boundary Value Problem

    You are right Wrobel. I overlooked that U is negative (the assumption). Sorry. The result now is consistent with an example that I have. u" + 4u = x^2 , u(0)=u(1)=0 Solution: u(x) = (2x^2 + sin(1-2x)/sin(1) - 1)/8 Lower bound solution F=4, G=1 U" + 4U = 1 , U(0)=U(1)=0 Solution...
  2. M

    A Boundary Value Problem

    Sorry to come back again to this thread. If I understand correctly, the mapping \mathcal F : W \rightarrow W where W=\{u\in C[0,1]\mid U\le u\le 0\} required the statement if h\le 0 then Ph=x\int_0^1d\xi\int_0^\xi h(s)ds-\int_0^xd\xi\int_0^\xi h(s)ds \le 0 . Also in the equation -U''=F...
  3. M

    A Boundary Value Problem

    Wow! What a solution. Thank you very much Wrobel. I need some time to properly understand the solution. Hope you don't mind if I ask again in case I do have problem understanding the argument. :smile:
  4. M

    A Boundary Value Problem

    Thanks. Interesting suggestion wrobel. So to which DE should I compare my equation ? Although I would prefer f(x) and g(x) to be general, I would still be content if f(x) is a monotonic increasing function since I'll be solving later on a specific DE with f(x) known.
  5. M

    A Boundary Value Problem

    I have a BVP of the form u" + f(x)u = g(x) , u(0)=u(1)= 0 where f(x) and g(x) are positive functions. I suspect that u(x) < 0 in the domain 0 < x < 1. How do I go proving this. I have try proving by contradiction. Assuming first u > 0 but I can't deduce that u" > 0 which contradict that u has...
  6. M

    Laplace transform to solve a nonhomogeneous equation

    Looks like you have a boundary value problem not initial value problem. If your DE is a linear constant coefficient, I think you still can solve it with Laplace transform.
  7. M

    Runge-Kutta Method - Need help with the calculus

    That explain partly. But why can't we also write the first term as f''(f(f)) and the second term as (f',f')f ?
  8. M

    Runge-Kutta Method - Need help with the calculus

    I got the expression from Prof. J.L. Butcher note, an authoritative person in Runge-Kutta method. That term is related to a rooted tree. Just google rooted tree Runge-Kutta for detail.
  9. M

    Runge-Kutta Method - Need help with the calculus

    When deriving the Runge-Kutta Method to solve y'=f(x) we need to use Taylor expansion. Hence we need to differentiate the function many times. y'(x)=f(y(x)) y''(x)=f'(y(x))y'(x) = f'(y(x))f(y(x)) y''' = f''(y(x))(f(y(x)),y'(x)) + f'(y(x))f'(y(x))y'(x) I can understand the second...
  10. M

    Role of eigenvalues in phase portraits

    Euler's formula e^{it}=\cos{t }+ i \sin{t}. So if the eigenvalue is a complex number, the solution will have sinusoidal functions I think.
  11. M

    Help with solving system of DE's

    Assuming that your system can be written as the matrix form \dot{X}=AX+F(t). , e.g. X=[x1 x2]t etc Then the general solution for this equation should be (if I'm not mistaken) X(t)=e^{At}C+e^{At}\int_0^t e^{-As}F(s) ds Your particular solution in this case is then X_p(t)=e^{At}\int_0^t...
  12. M

    MATLAB Matlab: Suppressing the output

    OK get it already from the other thread https://www.physicsforums.com/showthread.php?t=583140 Sorry about this.
  13. M

    MATLAB Matlab: Suppressing the output

    I get this example from >>help eval and add a semicolon. for n = 1:12 eval(['M' num2str(n) ' = magic(n)']); end The above commands display all 12 magic square. How do I suppress the output? I only want matlab to assign the variables not display them.
  14. M

    Solution for Sylvester Equation

    I don't think it is possible to express it as AX=B. Even to solve the Sylvester equation you have to diagonalize the matrices.
  15. M

    Differential equation in simple RC-circuit

    Laplace transform of your equation (*) should be sI+\frac{1}{RC}I=0 Solve for I and invert it. You should obtain the same answer.
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