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

Taylor's series method for simultaneous first order differential equations

Solved Example Problems

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The equations of the type dy / dx = f1 (x, y, z), dz/dx = f2 (x, y, z) with initial conditions y (x0) = y0, z (x0) = z0 can be solved by Taylor's series method.

TAYLOR'S SERIES METHOD FOR SIMULTANEOUS FIRST ORDER DIFFERENTIAL EQUATIONS

The equations of the type dy / dx = f1 (x, y, z), dz/dx = f2 (x, y, z) with initial conditions y (x0) = y0, z (x0) = z0 can be solved by Taylor's series method.

 

1. Solve the system of equations dy / dx = z - x2 dz/dx = y + x with  y (0) = 1, z (0) = 1 by taking h= 0.1, to get y (0.1) and z (0.1). Here, y and z are dependent variables and x is independent.

Solution: x0 = 0, y0 = 1, z0 = 1

Given:


 

Statistics and Numerical Methods: Unit V: Numerical Solution of Ordinary Differential Equations : Tag: : Solved Example Problems - Taylor's series method for simultaneous first order differential equations

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