Portal de Periódicos da CAPES

General methods in analysis, for the resolution of linear equations in finite differences and linear differential equations

1851; Royal Society; Volume: 5; Linguagem: Inglês

10.1098/rspl.1843.0185

2053-9134

Charles James Hargreave,

Induction Heating and Inverter Technology

The investigations presented in this paper consist of two parts; the first offers a solution, in a qualified sense, of the general linear equation in finite differences; and the second gives an analysis of the general linear differential equation with rational factors, so far as concerns its solution in series. The author observes that there does not at present exist any general method of solving linear equations in finite differences of an order higher than the first; and that with reference to such equations of the first order, we obtain insufficient forms which are intelligible only when the independent variable is an integer. It is in this qualified sense that the solutions proposed in this paper are to be taken; so that the first part of these investigations may be considered as an extension of this form of solution from the general equation of the first order to the general equation of the n th order.