coverage tests added

test/KdV.jl

@@ -45,7 +45,7 @@ using DiffEqOperators, OrdinaryDiffEq, LinearAlgebra
         @test soln(t) ≈ ϕ(x,t) atol = 0.01;
     end
 
-    # Using Biased Upwinds with 1 offside pont
+    # Using Biased Upwinds with 1 offside point
     A2 = UpwindDifference{Float64}(1,3,Δx,length(x),-1,offside=1);
     function KdV(du, u, p, t)
         bc = GeneralBC([0,1,-6*ϕ(-10,t),0,-1],[0,1,-6*ϕ(10,t),0,-1],Δx,3)
@@ -56,6 +56,7 @@ using DiffEqOperators, OrdinaryDiffEq, LinearAlgebra
     for t in 0:0.5:5
         @test soln(t) ≈ ϕ(x,t) atol = 0.01;
     end
+
     A3 = UpwindDifference{Float64}(1,3,Δx*ones(length(x)+1),length(x),-1,offside=1);
     function KdV(du, u, p, t)
         bc = GeneralBC([0,1,-6*ϕ(-10,t),0,-1],[0,1,-6*ϕ(10,t),0,-1],Δx,3)
@@ -66,6 +67,29 @@ using DiffEqOperators, OrdinaryDiffEq, LinearAlgebra
     for t in 0:0.5:5
         @test soln(t) ≈ ϕ(x,t) atol = 0.01;
     end
+
+    # Using Biased Upwinds with 2 offside points
+    A4 = UpwindDifference{Float64}(1,4,Δx,length(x),-1,offside=2);
+    function KdV(du, u, p, t)
+        bc = GeneralBC([0,1,-6*ϕ(-10,t),0,-1],[0,1,-6*ϕ(10,t),0,-1],Δx,3)
+        mul!(du,A4,bc*u)        
+    end
+    single_solition = ODEProblem(KdV, u0, (0.,5.));
+    soln = solve(single_solition,Tsit5(),abstol=1e-6,reltol=1e-6);
+    for t in 0:0.5:5
+        @test soln(t) ≈ ϕ(x,t) atol = 0.01;
+    end
+
+    A5 = UpwindDifference{Float64}(1,4,Δx,length(x),1,offside=2);
+    function KdV(du, u, p, t)
+        bc = GeneralBC([0,1,-6*ϕ(-10,t),0,-1],[0,1,-6*ϕ(10,t),0,-1],Δx,3)
+        mul!(du,-1*A5,bc*u)        
+    end
+    single_solition = ODEProblem(KdV, u0, (0.,5.));
+    soln = solve(single_solition,Tsit5(),abstol=1e-6,reltol=1e-6);
+    for t in 0:0.5:5
+        @test soln(t) ≈ ϕ(x,t) atol = 0.01;
+    end
 end
 
 # Conduct interesting experiments by referring to

test/heat_eqn.jl

@@ -33,7 +33,7 @@ end
     dx = 2π/(N-1)
     x = collect(-pi : dx : pi)
     u0 = @. -(x - 0.5)^2 + 1/12
-    B = CenteredDifference(1,2,dx,N)
+    B = CenteredDifference(1,2,dx,N-2)
     deriv_start, deriv_end = (B*u0)[1], (B*u0)[end]
 
     A = CenteredDifference(2,2,dx,N)
@@ -53,6 +53,23 @@ end
 
     # UpwindDifference with equal no. of primay wind and offside points should behave like a CenteredDifference
     A2 = UpwindDifference(2,1,dx,N,1,offside=1)
+    B2 = UpwindDifference(1,2,dx,N-2,1,offside=1)
+    deriv_start, deriv_end = (B2*u0)[1], (B2*u0)[end]
+    bc = NeumannBC((deriv_start,deriv_end),dx,1)
+
+    step(u,p,t) = A2*bc*u
+    heat_eqn = ODEProblem(step, u0, (0.,10.))
+    soln = solve(heat_eqn,Tsit5(),dense=false,tstops=0:0.01:10)
+
+    for t in 0:0.1:10
+        @test sum(first_order_coeffs_start .* soln(t)[1:4]) ≈ deriv_start atol=1e-1
+        @test sum(first_order_coeffs_end .* soln(t)[end-3:end]) ≈ deriv_end atol=1e-1
+    end
+    # Testing for 2 offside points against Standard Vector input
+    B3 = UpwindDifference(1,4,dx,N-2,-1,offside=2)
+    deriv_start, deriv_end = (-1*B3*u0)[1], (-1*B3*u0)[end]
+    bc = NeumannBC((deriv_start,deriv_end),dx,1)
+
     step(u,p,t) = A2*bc*u
     heat_eqn = ODEProblem(step, u0, (0.,10.))
     soln = solve(heat_eqn,Tsit5(),dense=false,tstops=0:0.01:10)
@@ -68,7 +85,7 @@ end
     dx = 2π/(N-1)
     x = collect(-pi : dx : pi)
     u0 = @. -(x - 0.5)^2 + 1/12
-    B = CenteredDifference(1,2,dx,N);
+    B = CenteredDifference(1,2,dx,N-2);
     deriv_start, deriv_end = (B*u0)[1], (B*u0)[end]
     params = [1.0,0.5]
 
@@ -92,13 +109,28 @@ end
     end
 
     # UpwindDifference with equal no. of primay wind and offside points should behave like a CenteredDifference
-    A2 = UpwindDifference(2,1,dx*ones(513),N,1,offside=1);
-    B2 = UpwindDifference(1,2,dx,N,1,offside=1)
+    A2 = UpwindDifference(2,1,dx*ones(N+1),N,1,offside=1)
+    B2 = UpwindDifference(1,2,dx*ones(N-1),N-2,1,offside=1)
     deriv_start, deriv_end = (B2*u0)[1], (B2*u0)[end]
     left_RBC = params[1]*u0[1] - params[2]*deriv_start
     right_RBC = params[1]*u0[end] + params[2]*deriv_end
     bc = RobinBC((params[1],-params[2],left_RBC), (params[1],params[2],right_RBC),dx,1);
-
+
+    step(u,p,t) = A2*bc*u
+    heat_eqn = ODEProblem(step, u0, (0.,10.));
+    soln = solve(heat_eqn,Tsit5(),dense=false,tstops=0:0.01:10);
+
+    for t in 0.2:0.1:9.8
+        @test params[1]*soln(t)[1] - params[2]*sum(first_order_coeffs_start .* soln(t)[1:4]) ≈ left_RBC atol=1e-1
+        @test params[1]*soln(t)[end] + params[2]*sum(first_order_coeffs_end .* soln(t)[end-3:end]) ≈ right_RBC atol=1e-1
+    end
+    # Testing for 2 offside points against Standard Vector input
+    B3 = UpwindDifference(1,4,dx*ones(N-1),N-2,-1,offside=2)
+    deriv_start, deriv_end = (-1*B3*u0)[1], (-1*B3*u0)[end]
+    left_RBC = params[1]*u0[1] - params[2]*deriv_start
+    right_RBC = params[1]*u0[end] + params[2]*deriv_end
+    bc = RobinBC((params[1],-params[2],left_RBC), (params[1],params[2],right_RBC),dx,1);
+
     step(u,p,t) = A2*bc*u
     heat_eqn = ODEProblem(step, u0, (0.,10.));
     soln = solve(heat_eqn,Tsit5(),dense=false,tstops=0:0.01:10);