Numerical Solutions of System of First Order Normalized Linear Differential Equations by Using Bernoulli Matrix Method

Abstract

Systems of first order differential equations have been arisen in science and engineering. Specially, the systems of normalized linear differential equations appear in differential geometry and kinematics problems. Solution of them is quite difficult analytically; therefore, numerical methods have need for the approximate solution. In this study, by means of a matrix method related to the truncated Bernoulli series we find the approximate solutions of the Frenet-Like system with variable coefficients upon the initial conditions. This method transforms the mentioned problem into a system of algebraic equations by using the matrix relations and collocation points; so, the required results along with the solutions are obtained and the usability of the method is discussed.

Keywords

• Approximate Solutions
• Curves of constant breadth
• Matrix Methods
• Systems of first order differential equations
• Bernoulli polynomials and series

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