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New dynamical equation for cracks
Physical Review Letters, 1991Summary: If a long-standing selection problem in brittle fracture is to be resolved, one must begin with dynamical equations suited to comparison with experiment. Such an equation is derived here in closed form by finding the energy flux to the tip of a slowly accelerating crack in a brittle strip.
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Dynamics of non‐linear wave equations
Mathematical Methods in the Applied Sciences, 2004AbstractWe present several stability/instability results for the ground‐state standing waves and high‐energy‐bound‐state standing waves for the NLKG, NLS and NLDW equations. At the end of the paper we present a number of open problems. Copyright © 2004 John Wiley & Sons, Ltd.
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Ordinary Differential Equations: Dynamical Systems
2007Ordinary differential equations (ode) are differential equations for functions which depend on one independent variable only. These ‘odes’ are simpler than partial differential equations which contain more than one independent variable. In almost all models or simulations independent variables are either time and/or space.
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Numerical Method for Time-Fractional Gas Dynamic Equations
Proceedings of the National Academy of Sciences India Section A Physical Sciences, 2018A. Prakash, Manoj Kumar
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings
Nature Nanotechnology, 2023Andrea Cordaro, Andrea Alu
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n0-order Δ-almost periodic functions and dynamic equations
, 2018Chao Wang, R. Agarwal, D. O’Regan
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DeepXDE: A Deep Learning Library for Solving Differential Equations
SIAM Review, 2021Lu Lu, George E Karniadakis
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