added tableaus for SSPRK methods

Author: ranocha

src/DiffEqDevTools.jl

@@ -59,6 +59,7 @@ export constructEuler, constructKutta3, constructRK4, constructRK438Rule,
        constructTanakaKasugaYamashitaYazaki6B, constructTanakaKasugaYamashitaYazaki6A,
        constructMikkawyEisa, constructChummund6, constructChummund62,
        constructHuta62, constructHuta6, constructRKF4, constructVerner7, constructVerner8,
-       constructVerner9, constructVerner6
+       constructVerner9, constructVerner6, constructSSPRK22, constructSSPRK33,
+       constructSSPRK43, constructSSPRK104
 
 end # module

src/ode_tableaus.jl

@@ -138,6 +138,73 @@ function constructRK438Rule(T::Type = Float64)
   return(ExplicitRKTableau(A,c,α,4))
 end
 
+"""
+Explicit SSP method of order 2 using 2 stages.
+"""
+function constructSSPRK22(T::Type = Float64)
+  A = [0 0
+       1 0]
+  c = [0; 1]
+  α = [1//2; 1//2]
+  A = map(T,A)
+  α = map(T,α)
+  c = map(T,c)
+  return(ExplicitRKTableau(A,c,α,2))
+end
+
+"""
+Explicit SSP method of order 3 using 3 stages.
+"""
+function constructSSPRK33(T::Type = Float64)
+  A = [0 0 0
+       1 0 0
+       1//4 1//4 0]
+  c = [0; 1; 1//2]
+  α = [1//6; 1//6; 2//3]
+  A = map(T,A)
+  α = map(T,α)
+  c = map(T,c)
+  return(ExplicitRKTableau(A,c,α,3))
+end
+
+"""
+Explicit SSP method of order 3 using 4 stages.
+"""
+function constructSSPRK43(T::Type = Float64)
+  A = [0 0 0 0
+       1//2 0 0 0
+       1//2 1//2 0 0
+       1//6 1//6 1//6 0]
+  c = [0; 1//2; 1; 1//2]
+  α = [1//6; 1//6; 1//6; 1//2]
+  A = map(T,A)
+  α = map(T,α)
+  c = map(T,c)
+  return(ExplicitRKTableau(A,c,α,3))
+end
+
+"""
+Explicit SSP method of order 4 using 10 stages.
+"""
+function constructSSPRK104(T::Type = Float64)
+  A = [0 0 0 0 0 0 0 0 0 0
+       1//6 0 0 0 0 0 0 0 0 0
+       1//6 1//6 0 0 0 0 0 0 0 0
+       1//6 1//6 1//6 0 0 0 0 0 0 0
+       1//6 1//6 1//6 1//6 0 0 0 0 0 0
+       1//15 1//15 1//15 1//15 1//15 0 0 0 0 0
+       1//15 1//15 1//15 1//15 1//15 1//6 0 0 0 0
+       1//15 1//15 1//15 1//15 1//15 1//6 1//6 0 0 0
+       1//15 1//15 1//15 1//15 1//15 1//6 1//6 1//6 0 0
+       1//15 1//15 1//15 1//15 1//15 1//6 1//6 1//6 1//6 0]
+  c = [0; 1//6; 1//3; 1//2; 2//3; 1//3; 1//2; 2//3; 5//6; 1]
+  α = [1//10; 1//10; 1//10; 1//10; 1//10; 1//10; 1//10; 1//10; 1//10; 1//10]
+  A = map(T,A)
+  α = map(T,α)
+  c = map(T,c)
+  return(ExplicitRKTableau(A,c,α,4))
+end
+
 """
 Implicit Euler Method
 """

test/ode_tableau_convergence_tests.jl

@@ -49,18 +49,34 @@ for i = 1:2 # 1 = num, 2 = ExplicitRK
   sim = test_convergence(dts,prob,tabalg)
   @test abs(sim.𝒪est[:l∞]-2) < testTol
 
+  tabalg = ExplicitRK(tableau=constructSSPRK22())
+  sim = test_convergence(dts,prob,tabalg)
+  @test abs(sim.𝒪est[:l∞]-2) < testTol
+
   # Order 3
 
   tabalg = ExplicitRK(tableau=constructBogakiShampine3())
   sim = test_convergence(dts,prob,tabalg)
   @test abs(sim.𝒪est[:l∞]-3) < testTol
 
+  tabalg = ExplicitRK(tableau=constructSSPRK33())
+  sim = test_convergence(dts,prob,tabalg)
+  @test abs(sim.𝒪est[:l∞]-3) < testTol
+
+  tabalg = ExplicitRK(tableau=constructSSPRK43())
+  sim = test_convergence(dts,prob,tabalg)
+  @test abs(sim.𝒪est[:l∞]-3) < testTol
+
   # Order 4
 
   tabalg = ExplicitRK(tableau=constructRKF4())
   sim = test_convergence(dts,prob,tabalg)
   @test abs(sim.𝒪est[:l∞]-4) < testTol
 
+  tabalg = ExplicitRK(tableau=constructSSPRK104())
+  sim = test_convergence(dts,prob,tabalg)
+  @test abs(sim.𝒪est[:l∞]-4) < testTol
+
   # Order 5
 
   dts = 1.//2.^(7:-1:4)