Compute weights for quadrature

Add function chebyshev_quadrature that computes the nodes and weights for qauss-chebyshev quadrature with weighting functions of the first and second kind.

Author: RJDennis

Project.toml

@@ -1,7 +1,7 @@
 name = "ChebyshevApprox"
 uuid = "17a596ad-87cd-578c-9b6d-01108c31dc04"
 authors = ["Richard Dennis <richard.dennis@glasgow.ac.uk>"]
-version = "0.1.12"
+version = "0.1.13"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/ChebyshevApprox.jl

@@ -8,6 +8,7 @@ include("chebyshev_nodes.jl")
 include("chebyshev_extrema.jl")
 include("chebyshev_extended.jl")
 include("vertesi_nodes.jl")
+include("chebyshev_quadrature.jl")
 include("normalize_node.jl")
 include("chebyshev_polynomial.jl")
 include("chebyshev_weights.jl")
@@ -25,6 +26,7 @@ export chebyshev_nodes,
        chebyshev_extrema,
        chebyshev_extended,
        vertesi_nodes,
+       chebyshev_quadrature,
        chebyshev_polynomial,
        chebyshev_weights,
        chebyshev_weights_extrema,

src/chebyshev_quadrature.jl

@@ -0,0 +1,37 @@
+function chebyshev_quadrature(node_type::Function,n::S,domain = [1.0,-1.0]) where {S <: Integer}
+
+  if n <= 0
+
+    error("The number of nodes must be positive.")
+  
+  end
+      
+  nodes   = zeros(n)
+  weights = zeros(n)
+
+  if node_type == chebyshev_nodes # weighting function is (1.0 .- nodes.^2).^(-1/2) -- (first kind)
+
+    for i = 1:n
+      nodes[i] = (domain[1]+domain[2])/2.0 - cos((i-0.5)*pi/n)*(domain[1]-domain[2])/2.0
+      weights[i] = pi/n
+    end
+
+    return nodes, weights
+
+  elseif node_type == chebyshev_extrema # weighting function is (1.0 .- nodes.^2).^(1/2) -- (second kind)
+
+    for i = 1:n
+      nodes[i] = (domain[1]+domain[2])/2.0 - cos((i-1)*pi/(n-1))*(domain[1]-domain[2])/2.0
+      weights[i] = (pi/(n-1))*sin(((i-1)/(n-1))*pi)^2
+    end
+
+    return nodes, weights
+    
+  else
+    
+    error("This node type is not supported")
+
+  end
+
+end
+