A New Concept for the Solution of Nonlinear Differential Equations

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Year:
2014
Type of Publication:
Article
Keywords:
Nonlinear Differential Equation, Nonlinearity Constant, Matrix Inner Product, Exact Solution, Approximate Solution
Authors:
Mohammed A. Azim
Journal:
IJISM
Volume:
2
Number:
5
Pages:
414-419
Month:
September
Abstract:
Present study introduces a concept for the solution of a class of nonlinear differential equations. An equation of this class is thought as a combination of some linear differential equations that rules the formation of complicated solution of the nonlinear equation from simple solutions of those linear equations. Exact or approximate analytic solutions of these nonlinear differential equations are obtained here by a method due to the new concept called the method of matrix inner product. Considered class of nonlinear differential equations encompasses both ordinary and partial differential equations with constant and variable coefficients. Apart from the obtained exact solutions, the approximate solutions of the nonlinear differential equations in general are found to be good at least in predicting the trend of the known solutions.

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