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Representation of linear PDEs with spatial integral terms as Partial Integral Equations
Sachin Shivakumar, Amritam Das, Matthew Peet
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial int…
math.NA2022
Computational stability analysis of PDEs with integral terms using the PIE framework
Sachin Shivakumar, Matthew Peet
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and th…