APPLICATION OF HYBRID LAPLACE TRANSFORM/ FINITE-DIFFERENCE METHOD TO TRANSIENT HEAT CONDUCTION PROBLEMS

REFERENCES

• B. Carnahan , H. A. Luther , and J. O. Wilkes , Applied Numerical Methods , pp. 454 – 461 , Wiley , New York , 1969 .
   Google Scholar
• E. L. Wilson and R. E. Nickell , Application of the Finite Element Method to Heat Convection Analysis, in Nuclear Engineering and Design , pp. 276–286, North-Holland . Amsterdam , 1966.
   Google Scholar
• H. S. Carslaw and J. C. Jaeger , Conduction of Heal in Solids, , 2d ed , Oxford University Press , London , 1959 .
   Google Scholar
• M. C. Bhattacharya , An Explicit Conditionally Stable Finite Difference Equation for Heat Conduction Problems , Int. J. Numer. Methods Eng. , vol. 21 , pp. 239 – 265 , 1985 .
   Web of Science ®Google Scholar
• W. Lick , Improved Difference Approximations to the Heat Equation , Int. J. Numer. Methods Eng. , vol. 21 , pp. 1957 – 1969 , 1985 .
   Google Scholar
• M. E. Gurtin , Variational Principles for Linear Initial-Value Problems , Q. Appl. Math. , vol. 22 , pp. 252 – 256 , 1964 .
   Google Scholar
• A. F. Emery and W. W. Carson , An Evaluation of the Use of the Finite Element Method in the Computation of Temperature , ASME J. Heat Transfer , vol. 39 , pp. 136 – 145 , 1971 .
   Web of Science ®Google Scholar
• W. Visser , A Finite Element Method for the Determination of Non-Stationary Temperature Distribution and Thermal Deformations , Proc. Conference on Matrix Methods in Structural Mechanics , pp. 925 – 943 , Air Force Institute of Technology, Wright Patterson Air Force Base , Dayton , Ohio , 1965 .
   Google Scholar
• J. C. Bruch and G. Zyvoloski , Transient Two-Dimensional Heat Conduction Problems Solved by the Finite Element Method , Int. J. Numer. Methods Eng. , vol. 8 , pp. 481 – 494 , 1974 .
   Google Scholar
• V. Rources and E. Aiarcon , Transient Heat Conduction Problems Using B.I.E.M. , Comput. Struct. , vol. 16 , pp. 717 – 730 , 1983 .
   Web of Science ®Google Scholar
• F. J. Rizzo and D. J. Shippy , A Method of Solution for Certain Problems of Transient Heat Conduction , AIAA J. , vol. 11 , pp. 2004 – 2009 , 1970 .
   Google Scholar
• J. A. Liggett and P. L.-F. Liu , Unsteady Flow in Confined Aquifers A Comparison of Two Boundary Integral Methods , Water Resour. Res. , vol. 15 , pp. 861 – 866 , 1979 .
   Web of Science ®Google Scholar
• A. H.-D. Cheng and J. A. Liggett , Boundary Integral Equation Method for Linear Porous-Elasticity with Applications to Soil Consolidation , Int. J. Numer. Methods Eng. , vol. 20 , pp. 255 – 278 , 1984 .
   Web of Science ®Google Scholar
• H. T. Chen , T. M. Chen , and C. K. Chen , Hybrid Laplace Transform/Finite Element Method for One-Dimensional Transient Heat Conduction Problems , Comput. Methods Appl. Mech. Eng. , vol. 63 , pp. 83 – 95 , 1987 .
   Web of Science ®Google Scholar
• G. E. Myers , Analytical Methods in Conduction Heat Transfer , McGraw-Hill , New York , 1971 .
   Google Scholar
• G. E. Myers , Finite-Difference/Finite Element Class Notes , University of Wisconsin , Madison , 1978 .
   Google Scholar
• G. E. Myers , The Critical Time Step for Finite-Element Solutions to Two-Dimensional Heat-Conduction Transients , ASME J. Heat Transfer , vol. 100 , pp. 120 – 127 , 1978 .
   Web of Science ®Google Scholar
• H. T. Ceylan , Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs , Ph.D. thesis , Mechanical Engineering Department. University of Wisconsin , Madison , 1979 .
   Google Scholar
• G. E. Bell , A Method for Treating Boundary Singularities in Time-Dependent Problems , TR/8, Department of Mathematics , Brunel University of Uxbridge , Middlesex , 1972 .
   Google Scholar
• F. Durbin , Numerical Inversion of Laplace Transforms Efficient Improvement to Dubner and Abate's Method , Comput. J. , vol. 17 , pp. 371 – 376 , 1973 .
   Web of Science ®Google Scholar
• W. M. Dubner and J. Abate , Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform , J. Assoc. Comput. Mach. , vol. 15 , pp. 115 – 123 , 1968 .
   Web of Science ®Google Scholar
• G. Honig and U. Hirdes , A Method for the Numerical Inversion of Laplace Transforms , J. Comput. Appl. Math. , vol. 9 , pp. 113 – 132 , 1984 .
   Google Scholar
• D. Shanks Nonlinear Transformation of Divergent and Slowly Convergent Sequences, J. Math. Phys. , vol. 34, pp. 1–42, 1955.
   Web of Science ®Google Scholar
• C. M. Bender and S. A. Orszag , Advanced Mathematical Methods for Scientists and Engineers , McGraw-Hill , New York , 1978 .
   Google Scholar
• M. D. Mikhailov and M. N. Ozisik , General Solution of One Dimensional, Time De pendent Coupled Heat Flow Systems , Int. Comm. Heat Mass Transfer , vol. 12 , pp. 393 – 404 , 1985 .
   Web of Science ®Google Scholar