Comments (8)
Agreed, but we please write those equations in the weak PDE form so it's easier to do the translation. To keep things simple, it's just the heat equation $ u_t = \sigma(x)u_{xx} $. There are some heat equation tests already:
https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/test/heat_eqn.jl
but it never hurts to add more.
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Shouldn't that be
from diffeqoperators.jl.
Yes thanks. Fixed.
from diffeqoperators.jl.
Maybe we can put in comments in the tests that mention both the PDE and stochastic process forms. Economists/finance people will find it much easier to think in terms of stochastic processes than the resulting PDEs. Also, don't forget that those are frequently NOT the PDEs that would come out of the discretized operators (e.g. backwards equations are different and the variational-inequalities that come out of stopping problems are also very different from that).
from diffeqoperators.jl.
Note, given the grid x_grid
to find the discretized sigma(x_grid)' * DerivativeOperator(...) * sigma(x_grid)
where the parameters for the derivative operator are the same as the one without the changing variance.
from diffeqoperators.jl.
Correction, you need the u
in there to apply the operator.
sigma(x_grid)' * DerivativeOperator(...) * u * sigma(x_grid)
from diffeqoperators.jl.
Note: only test the absorbing barrier with a value of 0 for now.
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Again, come back to this after #51 is complete.
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Related Issues (20)
- Performance issues with nonlinear_diffusion! HOT 4
- Fix symbolic arrays test to allow MTK v5.21.0 HOT 7
- UndefVarError: dereference not defined when precompiling DiffEqOperators (Win10, julia 1.6.1-2) HOT 7
- Version Compatibility? HOT 1
- Error defining second-order differential HOT 8
- The latest versions of LoopVectorization (0.12.80-81) are not compatible and cause errors HOT 1
- Noob Help: Simple, Linear, Inhomogenous PDE HOT 3
- concretization of High Dimension PDE HOT 2
- LoopVectorization break HOT 5
- Unexpected concretization of Laplace operator HOT 3
- v4.35.0 failed to release HOT 2
- Feature request: Support Summation-By-Parts operators HOT 4
- Support Unitful HOT 6
- Incorrect boundary padded vector with composed PeriodicBC on 2d data HOT 6
- Implementing Drift-Diffusion model in higher dimensions HOT 3
- Uninitialized field `opnorm` in JacVecOperator HOT 4
- SplitODEProblem broken for MatrixFreeOperator HOT 3
- ERROR: LoadError: Some tests did not pass: 30 passed, 0 failed, 4 errored, 4 broken. HOT 18
- Warning related to "LoopVectorization.check_args"
- Lots of precompilation errors and noise HOT 7
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