Calculation and approximation of the cnoidal function in cnoidal wave theory

A concise method for calculating the cnoidal function in cnoidal wave theory is presented. The method is based on the “precise integration method” and an improvement on the data preliminary treatment is employed to ensure the precision. For practical usage, a trigonometric function approximation expression for the cnoidal function is provided with brief verification. When the modulus of the wave is less than 0.95, the maximum error and absolute average error are acceptable for engineering.

► We present a concise method for calculating the cnoidal function.
► Data preliminary treatment is necessary to diminish the error bound.
► Trigonometric expression in approximating the cnoidal function is accurate but highly applicable in industry.