A child prodigy born in Australia, Tao, 50, is now at the top of his field at the University of California at Los Angeles, working in the rarefied realms of partial differential equations or harmonic ...

Abstract: This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, which is a mathematical tool able to ...

This paper develops ellipticity estimates and discretization error bounds for elliptic equations (with lower-order terms) that are reformulated as a least-squares ...

In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve ...

This is a preview. Log in through your library . Abstract This paper is concerned with oscillation of a certain class of second-order differential equations with a sublinear neutral term. Two ...

This course provides an introduction to topics involving ordinary differential equations. Emphasis is placed on the development of abstract concepts and applications for first-order and linear ...

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 ...

Abstract: We present a series of hybrid predictor-based third derivative linear multistep algorithms for solving stiff initial value problems in ordinary differential equations. The third-order ...