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The simultaneous population balance equation (PBE) incorporating diverse particulate process aggregation, breakage, growth, nucleation and source is a long-standing and significant problem in the field of particulate sciences such as pharmaceutical industry, chemical engineering, astrophysics and biology. Owing to the complex and nonlinear nature of the governing equations, finding an analytical solution is quite challenging for empirical kernels. In this work, simultaneous PBEs are solved using sectional and semi-analytical techniques. The performance, adaptability and accuracy of both methods for solving simultaneous PBEs are discussed in detail. The iterative semi-analytical scheme for solving simultaneous PBE is introduced, and a detailed convergence analysis using Banach fixed point theory is also presented. Both the schemes are further extended to solve simultaneous PBE in multi-dimensions. Performance analysis is also executed for multi-dimensional models. This article is a comprehensive study on various solution techniques for solving simultaneous PBEs. Therefore, it will be beneficial for the researchers working in industry and computational fluid dynamics modelling to identify the best method according to their requirements. [ABSTRACT FROM AUTHOR]