LEADER 04572nam 2200601 a 450 001 9910830662103321 005 20230421055220.0 010 $a1-283-10099-1 010 $a9786613100993 010 $a1-118-03146-6 010 $a1-118-03321-3 035 $a(CKB)3400000000000330 035 $a(EBL)699908 035 $a(OCoLC)705353441 035 $a(SSID)ssj0000506342 035 $a(PQKBManifestationID)11344038 035 $a(PQKBTitleCode)TC0000506342 035 $a(PQKBWorkID)10513825 035 $a(PQKB)11493327 035 $a(MiAaPQ)EBC699908 035 $a(EXLCZ)993400000000000330 100 $a19930113d1993 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe mollification method and the numerical solution of ill-posed problems$b[electronic resource] /$fDiego A. Murio 210 $aNew York $cWiley$dc1993 215 $a1 online resource (272 p.) 300 $a"A Wiley interscience publication." 311 $a0-471-59408-3 320 $aIncludes bibliographical references (p. 232-248) and index. 327 $aThe Mollification Method and the Numerical Solution of Ill-Posed Problems; Contents; Preface; Acknowledgments; 1. Numerical Differentiation; 1.1. Description of the Problem; 1.2. Stabilized Problem; 1.3. Differentiation as an Inverse Problem; 1.4. Parameter Selection; 1.5. Numerical Procedure; 1.6. Numerical Results; 1.7. Exercises; 1.8. References and Comments; 2. Abel's Integral Equation; 2.1. Description of the Problem; 2.2. Stabilized Problems; 2.3. Numerical Implementations; 2.4. Numerical Results and Comparisons; 2.5. Exercises; 2.6. References and Comments 327 $a3. Inverse Heat Conduction Problem3.1. One-Dimensional IHCP in a Semi-infinite Body; 3.2. Stabilized Problems; 3.3. One-Dimensional IHCP with Finite Slab Symmetry; 3.4. Finite-Difference Approximations; 3.5. Integral Equation Approximations; 3.6. Numerical Results; 3.7. Exercises; 3.8. References and Comments; 4. Two-Dimensional Inverse Heat Conduction Problem; 4.1. Two-Dimensional IHCP in a Semi-infinite Slab; 4.2. Stabilized Problem; 4.3. Numerical Procedure and Error Analysis; 4.4. Numerical Results; 4.5. Exercises; 4.6. References and Comments 327 $a5. Applications of the Space Marching Solution of the IHCP5.1. Identification of Boundary Source Functions; 5.2. Numerical Procedure; 5.3. IHCP with Phase Changes; 5.4. Description of the Problems; 5.5. Numerical Procedure; 5.6. Identification of the Initial Temperature Distribution; 5.7. Semi-infinite Body; 5.8. Finite Slab Symmetry; 5.9. Stabilized Problems; 5.10. Numerical Results; 5.11. Exercises; 5.12. References and Comments; 6. Applications of Stable Numerical Differentiation Procedures; 6.1. Numerical Identification of Forcing Terms; 6.2. Stabilized Problem; 6.3. Numerical Results 327 $a6.4. Identification of the Transmissivity Coefficient in the One-Dimensional Elliptic Equation6.5. Stability Analysis; 6.6. Numerical Method; 6.7. Numerical Results; 6.8. Identification of the Transmissivity Coefficient in the One-Dimensional Parabolic Equation; 6.9. Stability Analysis; 6.10. Numerical Method; 6.11. Numerical Results; 6.12. Exercises; 6.13. References and Comments; Appendix A. Mathematical Background; A.1. Lp Spaces; A.2. The Hilbert Space L2(?); A.3. Approximation of Functions in L2(?); A.4. Mollifiers; A.5. Fourier Transform; A.6. Discrete Functions 327 $aA.7. References and CommentsAppendix B. References to the Literature on the IHCP; Index 330 $aUses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations. 606 $aNumerical analysis$xImproperly posed problems 606 $aInverse problems (Differential equations)$xNumerical solutions 615 0$aNumerical analysis$xImproperly posed problems. 615 0$aInverse problems (Differential equations)$xNumerical solutions. 676 $a515.353 676 $a515/.353 700 $aMurio$b Diego A.$f1944-$060772 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830662103321 996 $aMollification Method and the Numerical Solution of Ill-Posed Problems$9376064 997 $aUNINA