Quantum computing has emerged as a potent technology capable of solving certain problems more efficiently than classical computers. Among its many applications, it is emerging as a promising technology for solving partial differential equations (PDEs). The presently available variational-quantum-eigensolver (VQE) based techniques for solving multidimensional PDEs on noisy-intermediate-scale-quantum (NISQ) devices exhibit low accuracy and large execution time when benchmarked against classical analytical solutions. This work introduces a new approach for solving PDEs leveraging numerical instantiation and classical-to-quantum (C2Q) encoding. More specifically, we leverage the finite difference method (FDM) for discretization of PDEs, followed by an integration of C2Q encoding and numerical instantiation techniques for quantum circuit synthesis. As a case study, we have used multidimensional variants of the Poisson equation to evaluate our technique. For experimental evaluation, we used noise-free and noisy simulators from IBM-Qiskit. The preliminary results demonstrate that our approach offers higher accuracy, higher scalability, and improved execution time compared to VQE-based PDE solvers.