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Numerical methods in field of applied mathematics and applied physics are well known tools for solution of various disciplinary and interdisciplinary field problems with different boundary conditions such as solid mechanics, heat transfer, fluid mechanics and soil mechanics etc. This paper aims for successfully framework to get feasible one-dimensional solutions of field problems (i.e. solid mechanics) with finite difference method, finite element method and their comparison with analytical (exact) solutions. Comparisons of Finite difference method and Finite element method with analytical solution with various number of field node and mixed boundary conditions are expressed with individual potential. This work concludes with potential of finite element & finite difference method leads to same results irrespective of numbers of field nodes chosen for one-dimensional field problems. Research work carried foundation and reference for acceptability and feasibility in field of numerical methods to solve physical problem especially by finite element and finite difference method.



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