SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
Uniform approximation on [−1, 1] via discrete de la Vallée Poussin means
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A de la Vallée Poussin-type projection method at Jacobi zeros is introduced for Fredholm integral equations, with proven stability, convergence in weighted spaces, and reduced Gibbs effects compared to Lagrange-based methods.
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Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems
SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
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De la Vall\'ee Poussin type approximation for solving some Fredholm integral equations
A de la Vallée Poussin-type projection method at Jacobi zeros is introduced for Fredholm integral equations, with proven stability, convergence in weighted spaces, and reduced Gibbs effects compared to Lagrange-based methods.