1- using  ModelingToolkit, OrdinaryDiffEq, ODEInterfaceDiffEq,  SpecialFunctions, LinearAlgebra
1+ using  ModelingToolkit, OrdinaryDiffEq, SpecialFunctions, LinearAlgebra
22using  Test
33
44#  Testing for α < 1
@@ -19,7 +19,7 @@ eqs += (gamma(9)*t^(8 - α)/gamma(9 - α)) + (3/2*t^(α/2)-t^4)^3 - x^(3/2)
1919sys =  fractional_to_ordinary (eqs, x, α, 10 ^- 7 , 1 )
2020
2121prob =  ODEProblem (sys, [], tspan)
22- sol =  solve (prob, radau5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
22+ sol =  solve (prob, RadauIIA5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
2323
2424for  time in  0 : 0.1 : 1 
2525    @test  isapprox (expect (time, α), sol (time, idxs= x), atol= 1e-7 )
@@ -32,7 +32,7 @@ eqs += (gamma(9)*t^(8 - α)/gamma(9 - α)) + (3/2*t^(α/2)-t^4)^3 - x^(3/2)
3232sys =  fractional_to_ordinary (eqs, x, α, 10 ^- 7 , 1 ; matrix= true )
3333
3434prob =  ODEProblem (sys, [], tspan)
35- sol =  solve (prob, radau5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
35+ sol =  solve (prob, RadauIIA5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
3636
3737for  time in  0 : 0.1 : 1 
3838    @test  isapprox (expect (time, α), sol (time, idxs= x), atol= 1e-7 )
@@ -44,7 +44,7 @@ eqs += (gamma(9)*t^(8 - α)/gamma(9 - α)) + (3/2*t^(α/2)-t^4)^3 - x^(3/2)
4444sys =  fractional_to_ordinary (eqs, x, α, 10 ^- 7 , 1 )
4545
4646prob =  ODEProblem (sys, [], tspan)
47- sol =  solve (prob, radau5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
47+ sol =  solve (prob, RadauIIA5 (), saveat= timepoint, abstol =  1e-10 , reltol =  1e-10 )
4848
4949for  time in  0 : 0.1 : 1 
5050    @test  isapprox (expect (time, α), sol (time, idxs= x), atol= 1e-7 )
@@ -58,7 +58,7 @@ tspan = (0., 220.)
5858
5959sys =  fractional_to_ordinary ([1  -  4 * x +  x^ 2  *  y, 3 * x -  x^ 2  *  y], [x, y], [1.3 , 0.8 ], 10 ^- 8 , 220 ; initials= [[1.2 , 1 ], 2.8 ], matrix= true )
6060prob =  ODEProblem (sys, [], tspan)
61- sol =  solve (prob, radau5 (), abstol =  1e-8 , reltol =  1e-8 )
61+ sol =  solve (prob, RadauIIA5 (), abstol =  1e-8 , reltol =  1e-8 )
6262
6363@test  isapprox (1.0097684171 , sol (220 , idxs= x), atol= 1e-5 )
6464@test  isapprox (2.1581264031 , sol (220 , idxs= y), atol= 1e-5 )
7575
7676sys =  linear_fractional_to_ordinary ([3 , 2.5 , 2 , 1 , .5 , 0 ], [1 , 1 , 1 , 4 , 1 , 4 ], 6 * cos (t), 10 ^- 5 , 5000 ; initials= [1 , 1 , - 1 ])
7777prob =  ODEProblem (sys, [], tspan)
78- sol =  solve (prob, radau5 (), abstol =  1e-5 , reltol =  1e-5 )
78+ sol =  solve (prob, RadauIIA5 (), abstol =  1e-5 , reltol =  1e-5 )
7979
8080@test  isapprox (expect (5000 ), sol (5000 , idxs= x_0), atol= 1e-5 )
8181
8282msys =  linear_fractional_to_ordinary ([3 , 2.5 , 2 , 1 , .5 , 0 ], [1 , 1 , 1 , 4 , 1 , 4 ], 6 * cos (t), 10 ^- 5 , 5000 ; initials= [1 , 1 , - 1 ], matrix= true )
8383mprob =  ODEProblem (sys, [], tspan)
84- msol =  solve (prob, radau5 (), abstol =  1e-5 , reltol =  1e-5 )
84+ msol =  solve (prob, RadauIIA5 (), abstol =  1e-5 , reltol =  1e-5 )
8585
8686@test  isapprox (expect (5000 ), msol (5000 , idxs= x_0), atol= 1e-5 )
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