# Questions tagged [nonlinear-equations]

Solution of nonlinear systems of equations. The equations might be algebraic or differential equations.

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### Solving a linear equation system with pure Neumann condition

I am trying to solve a linear equation system $\textbf{A}\textbf{x}=\textbf{b}$, e.g. a Poisson equation discretized in strong form, using biCGstab method. Since there are only natural Neumann ...
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### Solving a non-linear heat equation with the galerkin method gives negative values

I am trying to solve a non-linear time-dependent heat equation $$\partial_tT=\nabla \left(k_T(T)\nabla T\right) + f$$ using the galerkin method, with neumann boundary conditions. For linearization of ...
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### When is Newton-Krylov not an appropriate solver?

Recently I have been comparing different non-linear solvers from scipy and was particularly impressed with the Newton-Krylov example in the Scipy Cookbook in which they solve a second order ...
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### Strong coupling of a non-linear multiphysic problem: failure with Newton Raphson method

I am trying to solve a multiphysic problem using finite elements and a Newton Raphson solution scheme. I have two non-linear subsystems that are coupled bi-directionally. The first subsystem includes ...
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### Solving system of 7 nonlinear algebraic equations symbolically

I have a system of seven nonlinear equations that I want to find their symbolic solutions. The solution will depend on the parameter K, and I should have different solutions by varying the parameter. ...
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### 2d Euler manufactured solutions

Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?