Create MOLfornberg_weights.jl

tests for fornberg updated fornberg algorithm

Author: yewalenikhil65

test/pde_systems/MOLfornberg_weights.jl

@@ -0,0 +1,30 @@
+using Test, LinearAlgebra
+using MethodOfLines
+
+@testset "finite-difference weights from fornberg(1988) & fornberg(2020)" begin
+    order = 2; z = 0.0; x = [-1, 0, 1.0];
+    @test MethodOfLines.calculate_weights(order, z, x) == [1,-2,1]  # central difference of second-derivative with unit-step
+
+    order = 1; z = 0.0; x = [-1., 1.0];
+    @test MethodOfLines.calculate_weights(order, z, x) == [-0.5,0.5] # central difference of first-derivative with unit step
+
+    order = 1; z = 0.0; x = [0, 1];
+    @test MethodOfLines.calculate_weights(order, z, x) == [-1, 1] # forward difference
+
+    order = 1; z = 1.0; x = [0, 1];
+    @test MethodOfLines.calculate_weights(order, z, x) == [-1, 1] # backward difference
+
+    # forward-diff of third derivative with order of accuracy == 3
+    order = 3; z = 0.0; x = [0,1,2,3,4,5]
+    @test MethodOfLines.calculate_weights(order, z, x) == [-17/4,	71/4	,−59/2,	49/2,	−41/4,	7/4]
+    
+    order = 3; z = 0.0; x = collect(-3:3)
+    d, e = MethodOfLines.calculate_weights(order, z, x;dfdx = true)
+    @test d ≈ [-167/18000, -963/2000, -171/16,0,171/16,963/2000,167/18000]
+    @test e ≈ [-1/600,-27/200,-27/8,-49/3,-27/8,-27/200,-1/600]
+    
+    order = 3; z = 0.0; x = collect(-4:4)
+    d, e = MethodOfLines.calculate_weights(order, z, x;dfdx = true)
+    @test d ≈ [-2493/5488000, -12944/385875, -87/125 ,-1392/125,0,1392/125,87/125,12944/385875,2493/5488000]
+    @test e ≈ [-3/39200,-32/3675,-6/25,-96/25,-205/12, -96/25, -6/25,-32/3675,-3/39200]
+end