Physics-informed neural networks (PINNs) have demonstrated significant promise in addressing partial differential equations (PDEs) in recent years. However, PINNs face challenges such as high computational cost, low accuracy, and poor scalability. To tackle these challenges, physics-encoded recurrent convolutional neural network (PeRCNN) have been proposed as a discrete learning model, which integratively incorporates a specific physical framework within the neural network. Compared to the continuous learning models like PINNs, PeRCNN defines its loss function as the aggregate of discretized PDE residuals, where the network incorporates the initial and boundary conditions (I/BCs) in a defined manner to ensure strict compliance. Despite these advantages, PeRCNN often fails to converge when solving PDEs with large time steps, and an imbalance problem in the loss functions at different time steps has been observed. To address these issues, a novel method named MtS-PeRCNN is proposed, which utilizes a multi-time stepping weight updates algorithm. Experimental results demonstrate that MtS-PeRCNN significantly improves accuracy and extrapolability in solving PDEs, outperforming the baseline PeRCNN by one to two orders of magnitude. Moreover, MtS-PeRCNN successfully overcomes the convergence issues encountered with large time steps.