Explicit Gaussian quadrature rules for C1C1 cubic splines with symmetrically stretched knot sequences

• The paper provides expressions for quadrature rules on the space of C1C1 cubic splines with non-uniform, symmetrically stretched knot sequences.
• Any function from the space is exactly integrated by the rule.
• The quadrature nodes and weights are derived via explicit recursion formulae, with no intervention of any numerical solver.
• The rule is optimal, i.e. it requires minimal number of nodes.

We provide explicit expressions for quadrature rules on the space of C1C1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.