Introduces semilinear order conditions for Runge-Kutta methods on stiff semilinear ODEs via orthogonality relations and rooted trees, proving uniform global error bounds independent of stiffness.
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RepNN reparameterizes the first hidden layer of DNNs to enable adaptive frequency scaling, improving accuracy on oscillatory and multiscale functions with minimal extra cost.
A stable and convergent finite element scheme is developed for the variable-order time-fractional incompressible MHD equations, with experiments showing the impact of variable orders on energy and enstrophy.
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A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
Introduces semilinear order conditions for Runge-Kutta methods on stiff semilinear ODEs via orthogonality relations and rooted trees, proving uniform global error bounds independent of stiffness.
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Numerical Analysis of a Variable-Order Time-Fractional Incompressible Magnetohydrodynamics System
A stable and convergent finite element scheme is developed for the variable-order time-fractional incompressible MHD equations, with experiments showing the impact of variable orders on energy and enstrophy.