Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Delay differential equations (DDEs) extend the classical framework of differential equations by incorporating terms that depend on past states, thus capturing the intrinsic time delays found in many ...

Runge-Kutta methods applied to stiff systems in singular perturbation form are shown to give accurate approximations of phase portraits near hyperbolic stationary points. Over arbitrarily long time ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

Mean field-type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ were recently introduced by Lasry and Lions. Under suitable assumptions, ...