A Symbolic Algorithm for Solving Two-Point BVPs on

A Symbolic Algorithm for Solving Two-Point BVPs on the Operator Level


 

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f q A + D A aÙ

` f p A - D aÙ

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f q A + D A aÙ

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fq

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f q + ` f p A - D aÙ

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aÙ

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f q + ` f p A - b IÙ

f M’ r A - aÙ

aÙ

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f q - aÙ

fq D A

x

=

HDML

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HDAL

fq

aÙ

*

fq A

x

=

x

=

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fq D A

*

x

=

HDAL

x

=

ƒ

0 ¼

The rules RA and AMA yield the S|polynomial: A ` f p A + B ` f p A - R aÙ

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f q A + R A aÙ

A ` f p A + B ` f p A - R aÙ

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f q A + R A aÙ

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fq *

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x

=

fq

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x

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A aÙ

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f q + B aÙ

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f q + A ` f p A + B ` f p A - R aÙ

A aÙ

*

f q + B aÙ

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f q - IÙ

A aÙ

*

f q + B aÙ

*

f q - H˜ f L R A + A ` f p A + B ` f p A

fM

®

*

*

x

=

R A + A ` fp A + B ` fp A

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f q + aÙ

fq A + B ` fp A

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f q + B b Ù* f r + aÙ

0

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HraL

x

=

HRAL

x

=

fq + A ` fp A + B ` fp A

*

HAMAL

HBMAL

x

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f q A + b Ù* f r A

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x

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x

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The rules BR and RR yield the S|polynomial: -B R + aÙ* 1q R2

H¼L

x

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x

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x

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H˜ 1L R - B R - aÙ 1q R2

x

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x

=

H˜ 1L R - b Ù* 1 r R - aÙ 1q R *

0

=

HbL

x

=

ƒ

´ Computed 233 S|polynomials in 129 seconds. ´ Reduced them in 3144 seconds. ´ All of them reduced to zero!

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