Numerical algorithms are required when the solutions to mathematical problems cannot be expressed analytically. Adaptive algorithms expend the... Show moreNumerical algorithms are required when the solutions to mathematical problems cannot be expressed analytically. Adaptive algorithms expend the right amount of computational e↵ort to meet the error tolerance–easy problems require less e↵ort and hard problems require more e↵ort. Here we introduce a new globally adaptive trapezoidal rule algorithm satisfies a general error criterion, which includes both absolute and relative error tolerances. Then we derive the computational cost of the new algorithm and the complexity of this problem. M.S. in Applied Mathematics, May 2018 Show less
