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Note 3: I also tried LaplaceTransform, but it is obvious that this equation does nto has a closed form solution, like this problemthis problem

Note 3: I also tried LaplaceTransform, but it is obvious that this equation does nto has a closed form solution, like this problem

Note 3: I also tried LaplaceTransform, but it is obvious that this equation does nto has a closed form solution, like this problem

    Bumped by Community user
    Bumped by Community user
    Bumped by Community user
    Bumped by Community user
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Note 1: In every time step, I want to determine $\lambda(t) $ numerically using \[Lambda][t_Real], where lies the problem. It is well known that when NDSolve uses (N)Integrate internally, we will suffer from such kind of difficult very often. However, the equation I want to solve contain parameter $\lambda(t)$ found by integrating a function of the intermediate solution of my NDSlove. Fortunately, the NIntegrate does not involve t variable, which can be regarded as the average value of ${dV \over dh}$. I believe this point causes these problems. I'm not sure whether I have some other mistakes.

Any ideas? Also any suggestionssuggestion for code improvements areis more than welcome!

Note 1: In every time step, I want to determine $\lambda(t) $ numerically using \[Lambda][t_Real], where lies the problem. It is well known that when NDSolve uses (N)Integrate internally, we will suffer from such kind of difficult very often. However, the equation I want to solve contain parameter $\lambda(t)$ found by integrating a function of the solution of my NDSlove. Fortunately, the NIntegrate does not involve t variable, which can be regarded as the average value of ${dV \over dh}$. I believe this point causes these problems. I'm not sure whether I have some other mistakes.

Any ideas? Also any suggestions for code improvements are more than welcome!

Note 1: In every time step, I want to determine $\lambda(t) $ numerically using \[Lambda][t_Real], where lies the problem. It is well known that when NDSolve uses (N)Integrate internally, we will suffer from such kind of difficult very often. However, the equation I want to solve contain parameter $\lambda(t)$ found by integrating a function of the intermediate solution of my NDSlove. Fortunately, the NIntegrate does not involve t variable, which can be regarded as the average value of ${dV \over dh}$. I believe this point causes these problems. I'm not sure whether I have some other mistakes.

Any ideas? Also any suggestion for code improvements is more than welcome!

1
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