This study evaluates the performance of advanced numerical techniques based on the block backward differentiation formula (BBDF) in solving therapy models for Chronic Lymphocytic Leukemia (CLL). The CLL treatment model uses deferential equations to illustrate the interactions between cancer cells and treatment. The approximation uses BBDF-based model known as diagonal implicit BBDF with intermediate points to capture the dynamic interactions between cancer cells, immune cells, and therapeutic agents. The effectiveness of the new solver is assessed by comparing its results with both analytical solutions and existing solver. The findings demonstrate that the new method is effective for solving CLL therapy models.