WOLFRAM|DEMONSTRATIONS PROJECT

Solution of a Boundary Value Problem Using the Differential Transformation Method

λ

0.2

N

10

linear case

nonlinear case

Consider the following two boundary value problems, the first linear and the second nonlinear: (1)

y''(x)+y'(x)+3y(x)=

λt

e

with

y(-1)=0

and

y(1)=1

, and (2)

y''(x)+3y'(x)y(x)=

λt

e

with

y(-1)=0

and

y(1)=1

.

This Demonstration applies the differential transformation method (DTM) to solve these two problems. You can vary the parameter

λ

as well as the order of the Taylor series expansion,

N

. Excellent agreement is obtained between the result of the DTM (blue dashed curve) and its shooting technique counterpart (red curve) for large values of

N

.