Abstarct: Abstract Cancer treatment has progressed considerably since the first radiation treatments in the late 1800s and the early chemotherapies derived from mustard gas in the 1920–40s [1, 2]. Although the number and types of therapies available for cancer treatment have dramatically expanded over the past century, the dosing and timing of administration are still relatively imprecise. Standard-of-care treatment regimens are baxsed on the results of expensive and time-consuming clinical trials that seek first to determine the maximum tolerated dose (Phase I) and then the expected efficacy for a patient (Phases II and III). In most cancers, the problem is further compounded when multiple therapies are prescribed. In treating leukemia, it is usually prescribed to take several drugs simultaneously or sequentially for combined treatments. Several preclinical studies have shown that the order and timing of specific targeted and cytotoxic therapies may not be optimal [3, 4], and clinically there is evidence for certain combinations of drugs for which the sequence of their administration can significantly affect their efficacies and toxicities [5]. Therefore, oncology is in desperate need of a practical and clinically relevant logical frxamework that allows the investigator to a priori computes the optimal therapeutic regimen on a patient-specific basis. Optimal control theory is a branch of mathematics that aims to optimize a solution to a dynamic system. Using optimal control theory to improve treatment regimens in oncology is not a new issue. In many early applications, this mathematical technique is used to work with commonly available data or to produce results that can eventually be used in a clinical environment. In this research, we have used a pseudo-spectral method baxsed on the integral operational matrix to calculate the amount of drug used during the maintenance treatment of acute lymphoblastic leukemia.