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Sorry, if this is a duplicate, I was not able to find a corresponding answer. The only question related to mine, as far as I can see it, is this one: How to solve algebra equations containing containing integration and parametersHow to solve algebra equations containing containing integration and parameters . But no answers were given. My problem: I have a nonlinear algebraic system for some unknown variables, say, $a_1$ and $a_2$, which are in a nonlinear integral of a function containing $a_1$ and $a_2$ over a region $\Omega$, e.g., an ellipse. The constant right hand side is also given. I really just have a nonlinear system. The integrals are not elementary, so I have to use some trick.

Sorry, if this is a duplicate, I was not able to find a corresponding answer. The only question related to mine, as far as I can see it, is this one: How to solve algebra equations containing containing integration and parameters . But no answers were given. My problem: I have a nonlinear algebraic system for some unknown variables, say, $a_1$ and $a_2$, which are in a nonlinear integral of a function containing $a_1$ and $a_2$ over a region $\Omega$, e.g., an ellipse. The constant right hand side is also given. I really just have a nonlinear system. The integrals are not elementary, so I have to use some trick.

Sorry, if this is a duplicate, I was not able to find a corresponding answer. The only question related to mine, as far as I can see it, is this one: How to solve algebra equations containing containing integration and parameters . But no answers were given. My problem: I have a nonlinear algebraic system for some unknown variables, say, $a_1$ and $a_2$, which are in a nonlinear integral of a function containing $a_1$ and $a_2$ over a region $\Omega$, e.g., an ellipse. The constant right hand side is also given. I really just have a nonlinear system. The integrals are not elementary, so I have to use some trick.

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Until now, I am able to treat this using FindRoot and Integrate, but already for the 2D example given below this is kind of slow. I dont know if there is a way to use NIntegrate there. AlternativeAlternatively, I tried a rudimentary Newton algorithm and seems ok, see code below.

Until now, I am able to treat this using FindRoot and Integrate, but already for the 2D example given below this is kind of slow. I dont know if there is a way to use NIntegrate there. Alternative, I tried a rudimentary Newton algorithm and seems ok, see code below.

Until now, I am able to treat this using FindRoot and Integrate, but already for the 2D example given below this is kind of slow. I dont know if there is a way to use NIntegrate there. Alternatively, I tried a rudimentary Newton algorithm and seems ok, see code below.

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