How to solve this equation?

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Ilias Bouchkira
Ilias Bouchkira 2021-8-17
编辑： Walter Roberson 2021-8-17
Hi everyone,
Please can someone tells me how to solve the following equation using a pre-defined solver, such as ode15s;
is there any tutorials, file exchange, youtube video that may help ?
thank you so much in advance,
regards;
  2 个评论
Wan Ji
Wan Ji 2021-8-17
编辑：Wan Ji 2021-8-17
Hey, friend! The equation you provided cannot be solved by ode solver. It is already a 1st-order linear nonhomogeneous partial differential equation. It looks like 2d advection equation. So you can solve it by finite difference method.
You may take a reference to advection-in-1d-and-2d
Ilias Bouchkira
Ilias Bouchkira 2021-8-17
Thank you so much for sharing the exchange code and for the answer!

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回答（1 个）

Walter Roberson
Walter Roberson 2021-8-17
编辑：Walter Roberson 2021-8-17
That is a Partial Differential Equation (PDE), and can only be solved with ODE approaches if k_b sigma^b mu_3 delta(L, W) are separable for the three variables, making it really a series of three ODE.
Notice that the left side has a partial with respect to t but the right does not mention t in any obvious way. Either t is hidden (such as in the definition of k_b) or else the derivative with respect to t has to be zero.
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Ilias Bouchkira
Ilias Bouchkira 2021-8-17
Thank you so much for the answer, actually, sigma_b and mu_3 depend on t;

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