The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can ...

Abstract: 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 ...

The man gazes straight ahead, his eyes as dark as coals. His nose juts prominently from his tan face, which has become creased with wrinkles over time. Tufts of gray hair sprout from his balding head.

ABSTRACT: We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We ...