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

The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 (34 pages) The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk ...

Boundary value problems for nonlinear partial differential equations form a cornerstone of modern mathematical analysis, bridging theoretical advancements and practical real-world applications. These ...

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet methods are shown to ...