It can take years for humans to solve complex scientific problems. With AI, it can take a fraction of the time.

Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential equations ...

The biggest is that the formula divides the result by two. Mr. Trump said this was chosen to be “kind,” essentially halving the calculated tariff rates.

The Euler-Maruyama method is applied to a simple stochastic differential equation (SDE) with discontinuous drift. Convergence aspects are investigated in the case, where the Euler-Maruyama method is ...

For deterministic differential equations, models (1), (3) and (4), we use the Euler’s method and for stochastic differential equations, we implement the Euler-Maruyama method.

Looking ahead, the integration of machine learning with differential equations presents exciting opportunities for financial mathematics. Machine learning algorithms can be used to approximate ...

Numerical solution of partial differential equations by the finite element method by Johnson, Claes, 1943- Publication date 1987 Topics Finite element method, Differential equations, Partial -- ...

The Gauss-Bonnet formula is a beautiful equation in differential geometry that asserts the equality of the integral of the Gauss curvature over a surface and a constant multiplied by the Euler ...

Key words: Lattice Boltzmann method, relaxation methods, adjoint method, optimal control, systems of conservation laws, Euler equations. 1 Introduction In this paper, numerical approaches for ...