Four computation methods of first order differential quotient value for the theoretical earth tide—wave separation, first order difference, zenith distane differential and interpolation differential—have been introduced.
The results of various methods compared with differential quotient values and fitting testhave been shown. The interval of first order differential method and the interpolation differential method are discussed.
The recognition and correction method for false point by using first order differential is introduced. It is stated that under heavy shock disturbance after processing with the first order differential the influence of random interference can be eliminated by average method for smoothing.
The covergency and stability of numerical solution in first order differential equation are studied in this paper. The optimal coefficients are determined, and 3 trongly stable formulas in two-step linear method are got.
Let Q(x), F(·) 6 C, f(x), h = h(x) 6 C' and f ≠ 0, then first order differential equation is integrable. This result indicates a series of new pracrical integrable types. Some classical and moden integrable results are derived.
The method of proof is based on the integration of a first order differential inequality for a certain time weighted surface measure associated with the solution in question.
The quasi-cylindrical problem is reduced to solving a phase-plane first order differential equation.
For reflection free amplification the solution of the complete system of equations differs only slightly from the solution of the approximate first order differential equations , even for very high nonlinearities.
An inverse spectral problem for a nonnormal first order differential operator
With the M-C model we arrive at a single first order differential equation, while for the D-P solid an algebraic constraint supplements the governing differential equation.