Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations

Solving higher order linear differential equations

Taylor's Series Method | Solved Example Problems

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Taylor's series method can be extended to higher order differential equations.

SOLVING HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

Taylor's series method can be extended to higher order differential equations. The higher order differential equations can be expressed as a system of first order differential equations and the technique discussed for system of equations can be applied to solve the system.

 

1. By Taylor's series method find y (0.1) given that y'' = y + xy', y (0) = 1, y' (0) = 0.

Solution: Here, x0 = 0, y0 = 1, y0 = 0


 

2. Evaluate the values of y (0.1) and y (0.2) given y''-x(y')2+ y2 = 0; y (0) = 1, y' (0) = 0, by using Taylor series method.

Solution:


 

Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Taylor's Series Method | Solved Example Problems - Solving higher order linear differential equations

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MA3251 2nd Semester 2021 Regulation M2 Engineering Mathematics 2 | 2nd Semester Common to all Dept 2021 Regulation