# Solution of a Boundary Value Problem Using the Differential Transformation Method

Solution of a Boundary Value Problem Using the Differential Transformation Method

Consider the following two boundary value problems, the first linear and the second nonlinear: (1) with and , and (2) with and .

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

λt

e

y(-1)=0

y(1)=1

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

λt

e

y(-1)=0

y(1)=1

This Demonstration applies the differential transformation method (DTM) to solve these two problems. You can vary the parameter as well as the order of the Taylor series expansion, . Excellent agreement is obtained between the result of the DTM (blue dashed curve) and its shooting technique counterpart (red curve) for large values of .

λ

N

N