Date

ode file

diffeq

y

y'

y'''

y''''

x start

x end

h

digits

terms

Rel error 1st iter

iterations

Final rel error

type pole

radius conv

order of pole

time

atsinc.savnnn

atsgen.savnnn

omnisode.savnnn

Comment

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.00001

50

30

10

0.25

8

30

32

Most frequent test file

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.00001

50

30

100

1.6

8

30

32

more iterations

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.00001

32

30

100

1.53

8

30

32

fewer digits

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.00001

32

20

100

1.05

8

30

32

fewer terms

sinmapz

diff(z,t,1)=sin(t)

“-cos(t)”

0.1

0.00001

50

30

10

0.25

8

30

32

Make sure can use other variables – usually use x and y

sing3map

diff(y,x,1)=-2/x/x/x

“1/x/x”

-1

0.00001

50

30

10

real

1.008

4.4

0.22

8

30

32

real pole

sing4map

diff(y,x,1)=-2x/(x*x+1)/(x*x+1)

“1/(x*x+1)

-2

0.00001

50

30

10

complex

2.25

3.5

8

30

32

complex pole

h3sinmap

diff(y,x,3)=sin(x)

“-cos(x)”

“sin(x)”

“cos(x)”

0.1

0.00001

50

30

10

none

0.31

8

30

32

higher order diffeq

diff2map

diff(y,x,3)=diff(y,x,1)

“-cos(x)”

“sin(x)”

“cos(x)”

0.1

0.00001

32

30

100

none

0.22

8

30

32

diff on rhs

addmap

diff(y,x,1)=sin(x)+cos(x)

“sin(x)-cos(x)

0

0.00001

32

30

100

none

2.16

8

30

32

add

submap

diff(y,x,1)=sin(x)-cos(x)

“-sin(x)-cos(x)

0

0.00001

32

30

100

none

1.07

8

30

32

subtract

multmap

diff(y,x,1)=x*x

“x^3/3”

0.1

0.00001

32

30

100

none

0.75

8

30

32

multiply

mult2map

diff(y,x,1)=sin(x)*cos(x)

“-cos(x)^2/2”

0.1

0.00001

32

30

100

none

2.69

8

30

32

multiply

divmap

diff(y,x,1)=sin(x)/cos(x)

“-log(abs(cos(x)))”

0.1

0.00001

32

30

100

none

2.76

8

30

32

divide

cosmap

diff(y,x,1)=cos(x)

“sin(x)”

0.1

0.00001

32

30

100

none

1.5

8

30

33

cosine (small fix in omnisode to set relative error to -1 if true val 0)

tanmap

diff(y,x,1)=tan(y)

"-log(abs(cos(x)))”

0

0.00001

32

30

100

none

2.09

8

30

33

tangent

expmap

diff(y,x,1)=exp(x)

“exp(x)”

1

0.00001

32

30

100

none

1.1

8

30

33

exp

logmap

diff(y,x,1)=log(x)

“x*log(x)-x”

20

0.00001

32

30

100

0.0004

none

0.65

8

30

33

log

sinhmap

diff(y,x,1)=sinh(x)

“cosh(x)”

0

0.00001

32

30

0

100

none

1.46

8

30

33

sinh

coshmap

diff(y,x,1)=cosh(x)

“sinh(x)

0.1

0.00001

32

30

0

100

none

1.44

8

30

33

cosh

tanhmap

diff(y,x,1)=tanh(x)

“log(cosh)”

0.1

0.00001

32

30

100

complex

1.57

2.18

2.12

8

30

33

tanh

arcsinmap

diff(y,x,1)=arcsin(x)

“x*arcsin(x)+sqrt(1-x*x)

0

0.00001

32

30

100

none

2.04

8

30

33

arcsin

arccosmap

diff(y,x,1)=arccos(x)

“x*arccos(x)-sqrt(1-x*x)

0.1

0.00001

32

30

100

real

3.8

84.1

2.08

8

30

33

arccos

arctanmap

diff(y,x,1)=arctan(x)

“x*arctan(x)-log(x*x+1)/2

0.1

0.00001

32

30

100

complex

1.003

0.9105

4.25

8

30

33

arctan

diffmap

diff(y,x,2)=diff(y,x,1)

“exp(x)”

1.1

0.00001

32

30

100

none

1.4

8

30

33

another diff on rhs

h3sinmap

diff(y,x,2)=sin(x)

“-cos(x)”

“sin(x)”

0.1

0.00001

32

30

100

none

1.74

8

30

33

another higher order diffeq

sing2map

diff(y,x,2)=1/(x*x+1)

“arctan(x)”

-2

0.00001

32

30

100

complex

2.24

2.17

1.18

8

30

33

another pole

sing5map

diff(y,x,1)=-3/x/x/x/x

“1/x/x/x”

-1

0.00001

32

30

100

real

1.01

5.63

1.72

8

30

33

another pole

sing6map

diff(y,x,1)=-4/x/x/x/x/x

“1/x/x/x/x”

-1

0.00001

32

30

100

real

1.01

6.82

1.79

8

30

33

another pole

diff0map

diff(y,x,1)=diff(y,x,0)

“exp(x)”

1.1

0.00001

32

30

100

none

0.72

9

31

34

fixed mistake in diff on rhs – also updated to GPL 3

diff2map

diff(y,x,3)=diff(y,x,1)

“-cos(x)”

0.1

0.00001

32

30

100

none

1.46

9

31

34

diff on rhs (fixed)

diffmap

diff(y,x,2)=diff(y,x,1)

“exp(x)”

1.1

0.00001

32

30

100

none

1.02

9

31

34

another diff on rhs (fixed)

h3sinmap

diff(y,x,3)=sin(x)

“-sin(x)”

“-cos(x)”

“sin(x)”

0.1

0.00001

32

30

100

none

0.24

9

31

34

had mistake in analytic solution – also used to set initial cond

mtest2map  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

0.00001

32

30

100

none

1.72

9

31

35

had idea om multiple equations – should have no effect on single

mtest2map  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

0.00001

32

30

100

none

1.72

9

31

35

2nd equation same problem – also works with equations reversed

complicatedmap A

X1' = 4*x2-2*x2'-2x1

x1=c1+6*c3*exp(-t)

x1'= -6*c3*exp(-t)

0.5

0.000000001

32

30

100

none

4.97

9

31

36

complicated c1=0.0001 c2 = 0.0002 c3 = 0.0003

complicatedmap B

X2'' = 3*x2'-2*x2-x1''-x1'-x1

x2=c1+c2*exp(2*t)+c3*exp(-t)

x2'=2+c2*exp(2*t)-c3*exp(-t)

0.5

0.000000001

32

30

100

none

4.97

9

31

36

slight modification for multiple equations

complicatedmap A

X1' = 4*x2-2*x2'-2x1

x1=c1+6*c3*exp(-t)

x1'= -6*c3*exp(-t)

0.5

0.00001

32

30

100

none

4.81

9

31

36

complicated c1=0.0001 c2 = 0.0002 c3 = 0.0003

complicatedmap B

X2'' = 3*x2'-2*x2-x1''-x1'-x1

x2=c1+c2*exp(2*t)+c3*exp(-t)

x2'=2+c2*exp(2*t)-c3*exp(-t)

0.5

0.00001

32

30

100

none

4.81

9

31

36

larger increment

sinmap

y'=sin(x)

y=-cos(x)

0.1

5.01

0.01

32

30

491

none

6.04

10

32

37

cleaned output; larger increment;rel err now %(*100);

mtest2map  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

10.01

0.01

32

30

100

none

14.73

10

32

37

larger increment

mtest2map  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

10.01

0.01

32

30

100

none

14.73

10

32

37

complicatedmap A

X1' = 4*x2-2*x2'-2x1

x1=c1+6*c3*exp(-t)

x1'= -6*c3*exp(-t)

0.5

5.01

0.001

32

30

4501

none

202.43

10

32

37

complicated c1=0.0001 c2 = 0.0002 c3 = 0.0003

complicatedmap B

X2'' = 3*x2'-2*x2-x1''-x1'-x1

x2=c1+c2*exp(2*t)+c3*exp(-t)

x2'=2+c2*exp(2*t)-c3*exp(-t)

0.5

5.01

0.001

32

30

4501

none

202.43

10

32

37

larger increment

diff0map

diff(y,x,1)=diff(y,x,0)

“exp(x)”

1.1

2.01

0.01

32

30

91

none

0.44

10

32

37

larger increment

diff2map

diff(y,x,3)=diff(y,x,1)

“-cos(x)”

0.1

2.01

0.01

32

30

191

none

3.59

10

32

38

cosmetic change & larger increment

diff2map

diff(y,x,3)=diff(y,x,1)

“-cos(x)”

0.1

2.001

0.001

32

30

1901

none

33.98

10

32

38

smaller increment

Vastly revised program – also supports maxima

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

1.0009

0.00001

32

30

10

none

0.14

23

45

51

retest with version supporting maxima also – greatly improved code

sinmax

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

1.0009

0.00001

32

30

10

none

4

23

45

51

same test with maxima

mtest2map  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

1.001

0.00001

32

30

10

none

0.17

23

45

51

maple 1st eq

mtest2map  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

1.001

0.00001

32

30

10

none

0.17

23

45

51

maple 2nd eq

mtest2max  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

1.001

0.00001

32

30

10

none

5

23

45

51

maxima 1st eq

mtest2max  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

1.001

0.00001

32

30

10

none

5

23

45

51

maxima 2nd eq – I want to check whether I really have fpprec set right

sing3map

diff(y,x,1)=-2/x/x/x

“1/x/x”

-1

-0.9999

0.00001

32

30

10

real

1

4.4

0.15

23

45

51

real pole

sing3max

diff(y,x,1)=-2/x/x/x

“1/x/x”

-1

-0.9999

0.00001

32

30

10

none

5

23

45

51

did not find pole – need to do more debugging on pole logic

sinmap

diff(y,x,1)=sin(x)

“-cos(x)'

0.1

0.1001

0.00001

100

30

10

none

0.15

29

51

57

what's in omnisode0006.tar.gz – does maple only give 32 digit on sin?

sinmap

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.1001

0.00001

32

30

10

none

0.14

29

51

57

almost same accuracy with Digits := 32 as Digits := 100

sinmax

diff(y,x,1)=sin(x)

“-cos(x)”

0.1

0.1001

0.00001

16

30

10

none

4

29

51

57

definitely determined maxima only gives 16 digits on trig-bfloat no use

sing3map

diff(y,x,1)=-2/x/x/x

“1/x/x”

-1

-0.9999

0.00001

100

30

10

real

1.008

4.4

0.16

29

51

57

real pole maple

sing3max

diff(y,x,1)=-2/x/x/x

“1/x/x”

-1

-0.9999

0.00001

16

30

10

real

1.008

4.4

5

29

51

57

real pole maxima

mtest2map  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

1.001

0.00001

32

30

10

none

0.2

29

51

57

maple 1st eq

mtest2map  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

1.001

0.00001

32

30

10

none

0.17

29

51

57

maple 2nd eq

mtest2max  A

diff(y2,x,1)=diff(y1,x,0)

y2=sin(x)

0.1

1.001

0.00001

16

30

10

none

5

29

51

57

maxima 1st eq

mtest2max  B

diff(y1,x,1)=-diff(y2,x,0)

y1=cos(x)

0.1

1.001

0.00001

16

30

10

none

5

29

51

57

maxima 2nd eq – I want to check whether I really have fpprec set right