A new technique for solving nonlinear differential equations encountered in modeling of neuroreceptor-binding ligands

1988 ◽  
Vol 35 (1) ◽  
pp. 762-766 ◽  
Author(s):  
S.-c. Huang ◽  
M.M. Bahn ◽  
M.E. Phelps
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
New Technique ◽  
A New Technique

A class of nonlinear heat-type equations and their multi-wave solutions by a generalized bilinear technique

2016 ◽  
Vol 30 (06) ◽  
pp. 1650067
Author(s):  
Jun-Rong Liu
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
New Technique ◽  
Bilinear Operators ◽  
Wave Solutions ◽  
Dependent Variables ◽  
A New Technique ◽  
Bilinear Equations

Multi-wave resonant solutions of a class of nonlinear heat-type equations are investigated by their corresponding generalized bilinear equations. We develop a new technique for searching for resonant solutions to those generalized bilinear equations, using the idea of weights of dependent variables. The results show that generalized bilinear operators and generalized bilinear equations are powerful and irreplaceable tools for dealing with nonlinear differential equations.

scholarly journals Short Communication: A technique for investigating nonlinear vibrations

2012 ◽  
Vol 34 (2) ◽  
pp. 135-138
Author(s):  
Nguyen Dong Anh
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Short Communication ◽  
Nonlinear Differential Equations ◽  
Duffing Oscillator ◽  
New Technique ◽  
Equivalent Linearization ◽  
Nonlinear Features ◽  
A New Technique ◽  
Main Ideas

In this short communication the main ideas of the method of equivalent linearization and dual conception are further extended to suggest a new technique for solving nonlinear differential equations. This technique allows improving the accuracy when the nonlinearity is strong and getting nonlinear features of responses. For illustration the Duffing oscillator is considered to demonstrate the effectiveness of the proposed technique.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

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