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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Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).
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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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Higher-order exponential Runge-Kutta Galerkin finite element method for semilinear parabolic problems with nonsmooth data
Proves that the p-th order EERK method for semilinear parabolic problems with initial regularity γ achieves convergence rate min(1 + γ/2 + ρ1(γ)/2, p).