coverage tests for biased Upwind

Author: mjsheikh

test/KdV.jl

@@ -41,7 +41,28 @@ using DiffEqOperators, OrdinaryDiffEq, LinearAlgebra
         @show maximum(soln(t)-ϕ(x,t))
     end
     =#
+    for t in 0:0.5:5
+        @test soln(t) ≈ ϕ(x,t) atol = 0.01;
+    end
 
+    # Using Biased Upwinds with 1 offside pont
+    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)
+        mul!(du,A2,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
+    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)
+        mul!(du,A3,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

test/heat_eqn.jl

@@ -92,7 +92,13 @@ end
     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);
+    A2 = UpwindDifference(2,1,dx*ones(513),N,1,offside=1);
+    B2 = UpwindDifference(1,2,dx,N,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);