Differential equation solving for continuous simulation

1972 ◽  
Vol 4 (1) ◽  
pp. 8-9 ◽  
Author(s):  
Walter L. Whipple
Keyword(s):  
Differential Equation ◽  
Continuous Simulation ◽  
Equation Solving

Developed Plate Expansion Using Geodesics

1984 ◽  
Vol 21 (04) ◽  
pp. 384-388
Author(s):  
John C. Clements
Keyword(s):  
Differential Equation ◽  
Numerical Quadrature ◽  
Developable Surface ◽  
Accuracy Control ◽  
Isometric Mapping ◽  
Variable Stepsize ◽  
Mapping Algorithm ◽  
Equation Solving ◽  
Expansion Procedure ◽  
The Relationship

This work is concerned with the application of a new isometric mapping algorithm to hull plate expansion procedures for ships with all or portions of the hull consisting of developable surfaces. The expansion procedure is based on the relationship between the ruling lines r⇀(s) generating the developable surface S⇀(s,t) and one additional geodesic g⇀(s) constructed within the surface as the solution of the differential equation det(g⇀'g⇀"n⇀) = 0 where n⇀ is the unit normal to S⇀ at g⇀. Precise accuracy control is achieved through the use of adaptive numerical quadrature and a variable stepsize differential equation solving routine.

scholarly journals NNC: A tool based on Grammatical Evolution for data classification and differential equation solving

SoftwareX ◽  
2019 ◽  
Vol 10 ◽  
pp. 100297
Author(s):  
Ioannis G. Tsoulos ◽  
Alexandros Tzallas ◽  
Dimitris Tsalikakis
Keyword(s):  
Differential Equation ◽  
Data Classification ◽  
Grammatical Evolution ◽  
Equation Solving

scholarly journals MATHEMATICAL DESCRIPTION OF DIFFERENTIAL EQUATION SOLVING ELECTRICAL CIRCUITS

2009 ◽  
Vol 18 (05) ◽  
pp. 985-991 ◽  
Author(s):  
K. NAKKEERAN
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Time Varying ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Electrical Circuits ◽  
Equation Solving ◽  
Low Pass ◽  
Working Principle

We show that the working principle of the differential equation solving analog electrical circuits is exactly the same as the Picard's method available for numerically solving the ordinary differential equations. The integrator circuit (low-pass filter) uses an initial condition and electrical input signal to generate the Maclaurin's series of a time varying function in recursion. This direct connection between the differential equation solving electrical circuits and Picard's method can be exploited to simplify the procedure of Picard's method to solve any order linear and nonlinear differential equations.

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