The Integral Fast Reactor (IFR) is an advanced nuclear energy system that incorporates a closed fuel cycle, enabling electricity generation, nuclear fuel recycling, and the transmutation of minor actinides. As the reactor operates, fissile isotopes in the fuel are progressively consumed, while fission products accumulate. These fission products not only pose a potential risk to reactor operational safety but also generate highly radioactive actinides with long half-lives. The JLAMT pre-processing modeling tool is utilized to construct a detailed model of the IFR core, which includes hundreds of hexagonal fuel assemblies, with precise geometric descriptions of each component. The JMCT software is then used to perform transport-burnup coupled calculations, yielding core-wide power distributions and isotopic changes across different burnup regions. These results provide valuable insights for core design optimization and the transmutation of minor actinides. By conducting core transport-burnup coupled calculations, detailed pin-by-pin power distributions and isotopic variations across different burnup regions are obtained. The visual outputs provide an intuitive understanding of the temperature and power distributions in the core at each burnup step. The Chebyshev Rational Approximation Method (CRAM) is employed to approximate the complex functions within the neutron transport equation, playing a crucial role in reactor burnup calculations, particularly in fuel management and power distribution. This method reduces computational complexity and enhances efficiency. In this study, the JMCT particle transport simulation software is used in conjunction with the CRAM to perform core burnup calculations, successfully reducing the dimensionality of the computational problem and significantly improving both the accuracy and efficiency of the results. Additionally, parallel computing techniques are applied by decomposing the computational process into subregions and utilizing varying numbers of computational cores to accelerate the calculations. This approach not only reduces computational time but also quantifies speedup ratios for different core configurations, further optimizing computational efficiency.