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One of the electromagnetic induction (EMI) schemes for submarine hydrocarbon reservoir exploration is the control source electromagnetic (CSEM) method. Despite the fact that the marine CSEM method has less accuracy compared to the seismic reflection measurements, it has reduced the cost of modeling and has a relatively high coverage speed. In this research, for 3D and 4D forward modeling of a hydrocarbon reservoir with a regular geometrical shape, the Fredholm integral equation (IE) of second order is used. Whereas for solving full integral equations high performance computers are needed and these computational costs are expensive, approximations are usually used to solve electromagnetic problems. The scope of this study is to utilize several approximation methods to solve the integral equation for 4D forward modeling of a regular geometrical shape reservoir using CSEM synthetic data. These approximation methods consist of T-matrix approximation (TMA), Extended Born approximation (EBA), and Born approximation (BA). To numerically verify the performance of the proposed approximations, the inverse modeling of the proposed methods is implemented and then tested in MATLAB. Our results show that the T-Matrix approximation has better accuracy and a wider electrical conductivity application range.