Abstract
In this study, we present a reliable numerical approximation of the some first order nonlinear ordinary differential equations with the mixed condition by the using a new Taylor collocation method. The solution is obtained in the form of a truncated Taylor series with easily determined components. Also, the method can be used to solve Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparing the methodology with some known techniques shows that the existing approximation is relatively easy and highly accurate.
Highlights
Nonlinear ordinary differential equations are frequently used to model a wide class of problems in many areas of scientific fields; chemical reactions, spring-mass systems bending of beams, resistor-capacitor-inductance circuits, pendulums, the motion of a rotating mass around another body and so forth 1, 2
We consider the solution y(x) defined by a truncated series (3) and we can convert to the matrix form y(x) X(x)Y
The principal advantage of this method, at the around x c, is the capability to succeed in the solution up to all term of Taylor expansion
Summary
Nonlinear ordinary differential equations are frequently used to model a wide class of problems in many areas of scientific fields; chemical reactions, spring-mass systems bending of beams, resistor-capacitor-inductance circuits, pendulums, the motion of a rotating mass around another body and so forth 1, 2. These equations here demonstrated their usefulness in ecology, economics, biology, astrophysics and engineering. Methods of solution for these equations are of great importance to engineers and scientists 3, 4. For our aim we consider the first order nonlinear ordinary differential equation of the form
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