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Full-Text Articles in Physical Sciences and Mathematics
A Numerical Method For Functional Hammerstein Integro-Differential Equations, L. Saeedi, A. Tari
A Numerical Method For Functional Hammerstein Integro-Differential Equations, L. Saeedi, A. Tari
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a numerical method is presented to solve functional Hammerstein integro-differential equations. The presented method combines the successive approximations method with trapezoidal quadrature rule and natural cubic spline interpolation to solve the mentioned equations. The existence and uniqueness of the problem is also investigated. The convergence and numerical stability of the problem are proved, and finally, the accuracy of the method is verified by presenting some numerical computations.
Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Ashley Montiforte
Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Ashley Montiforte
Master's Theses
Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.