Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

SIAM Journal on Applied Mathematics, Vol. 22, No. 4 (Jun., 1972), pp. 629-647 (19 pages) The two-time perturbation procedure is applied to a class of inhomogeneous initial boundary value problems for ...

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

Initial value problems for first order partial functional almost linear equations with unbounded delay are considered. The functional dependence is represented by the generalized Hale operator with ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...