Topic
Separable partial differential equation
About: Separable partial differential equation is a research topic. Over the lifetime, 5788 publications have been published within this topic receiving 174806 citations.
Papers published on a yearly basis
1 / 3
Papers
TL;DR: In this paper, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Abstract: Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential Equations V: Dependence on Initial Conditions and Parameters VI: Total and Partial Differential Equations VII: The Poincare-Bendixson Theory VIII: Plane Stationary Points IX: Invariant Manifolds and Linearizations X: Perturbed Linear Systems XI: Linear Second Order Equations XII: Use of Implicity Function and Fixed Point Theorems XIII: Dichotomies for Solutions of Linear Equations XIV: Miscellany on Monotomy Hints for Exercises References Index.
5,648 citations
TL;DR: In this article, the Fundamental Theorem of Calculus gives us an important connection between differential equations and integrals, and modern numerical methods automatically determine the step sizes hn = tn+1 − tn so that the estimated error in the numerical solution is controlled by a specified tolerance.
Abstract: together with the initial condition y(t0) = y0 A numerical solution to this problem generates a sequence of values for the independent variable, t0, t1, . . . , and a corresponding sequence of values for the dependent variable, y0, y1, . . . , so that each yn approximates the solution at tn yn ≈ y(tn), n = 0, 1, . . . Modern numerical methods automatically determine the step sizes hn = tn+1 − tn so that the estimated error in the numerical solution is controlled by a specified tolerance. The Fundamental Theorem of Calculus gives us an important connection between differential equations and integrals.
5,073 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 2 |
| 2023 | 11 |
| 2022 | 30 |
| 2021 | 1 |
| 2019 | 6 |