Computational methods for linear integral equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
2002
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 473 - 508 |
| Beschreibung: | XVIII, 508 S. graph. Darst. : 24 cm |
| ISBN: | 3764341920 0817641920 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014556884 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 020709s2002 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 964695685 |2 DE-101 | |
| 020 | |a 3764341920 |c (Basel ...) Pp. : EUR 129.00 |9 3-7643-4192-0 | ||
| 020 | |a 0817641920 |c (Boston) Pp. |9 0-8176-4192-0 | ||
| 035 | |a (OCoLC)48536698 | ||
| 035 | |a (DE-599)BVBBV014556884 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-634 |a DE-83 | ||
| 050 | 0 | |a QA431 | |
| 082 | 0 | |a 515/.45 |2 21 | |
| 084 | |a SK 640 |0 (DE-625)143250: |2 rvk | ||
| 084 | |a SK 920 |0 (DE-625)143272: |2 rvk | ||
| 084 | |a 65R20 |2 msc | ||
| 100 | 1 | |a Kythe, Prem K. |d 1930- |e Verfasser |0 (DE-588)12072362X |4 aut | |
| 245 | 1 | 0 | |a Computational methods for linear integral equations |c Prem K. Kythe ; Pratap Puri |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 2002 | |
| 300 | |a XVIII, 508 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 473 - 508 | ||
| 650 | 7 | |a Integraalvergelijkingen |2 gtt | |
| 650 | 4 | |a Integral equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Integralgleichung |0 (DE-588)4114426-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Integralgleichung |0 (DE-588)4114426-0 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pratap, Puri |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009898655 | ||
Datensatz im Suchindex
| _version_ | 1804129336629919744 |
|---|---|
| adam_text | IMAGE 1
?
PREM K. KYTHE
PRATAP PURI
COMPUTATIONAL METHODS FOR LINEAR INTEGRAL EQUATIONS
WITH 12 FIGURES
BIRKHAEUSER BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
PREFACE XI
NOTATION XV
1 INTRODUCTION 1
1.1 NOTATION AND DEFINITIONS 1
1.2 CLASSIFICATION 7
1.2.1 KINDS AND TYPES 7
1.2.2 CONVOLUTION OF KERNELS 13
1.3 FUNCTION SPACES 16
1.4 CONVERGENCE 20
1.5 INVERSE OPERATOR 21
1.6 NYSTROEM SYSTEM 23
1.7 OTHER TYPES OF KERNELS 28
1.7.1 NONDEGENERATE KERNELS 28
1.7.2 DEGENERATE KERNELS 31
1.8 NEUMANN SERIES 33
1.9 RESOLVENT OPERATOR 35
1.10 FREDHOLM ALTERNATIVE 40
2 EIGENVALUE PROBLEMS 44
2.1 LINEAR SYMMETRIE EQUATIONS 45
2.1.1 RITZ METHOD 46
2.1.2 METHOD OF MOMENTS 48
2.1.3 KELLOGG S METHOD 51
2.1.4 TRACE METHOD 52
2.2 RESIDUAL METHODS 55
2.2.1 COLLOCATION METHOD 55
V
IMAGE 3
VI CONTENTS
2.2.2 LEAST-SQUARES METHOD 57
2.2.3 GALERKIN METHOD 60
2.3 DEGENERATE KERNELS 63
2.4 REPLACEMENT BY A DEGENERATE KERNEL 67
2.5 BATEMAN S METHOD 72
2.6 GENERALIZED EIGENVALUE PROBLEM 77
2.7 APPLICATIONS 82
3 EQUATIONS OF THE SECOND KIND 90
3.1 FREDHOLM EQUATIONS 90
3.1.1 SYSTEMS OF INTEGRAL EQUATIONS 91
3.1.2 TAYLOR S SERIES METHOD 93
3.2 VOLTERRA EQUATIONS , 96
3.2.1 QUADRATURE METHODS 98
3.2.2 BLOCK-BY-BLOCK METHOD 102
4 CLASSICAL METHODS FOR FK2 106
4.1 EXPANSION METHOD 106
4.2 PRODUCT-INTEGRATION METHOD 108
4.3 QUADRATURE METHOD 111
4.4 DEFERRED CORRECTION METHODS 115
4.5 A MODIFIED QUADRATURE METHOD 121
4.6 COLLOCATION METHODS 123
4.7 ELLIOTT S MODIFIKATION 127
5 VARIATIONAL METHODS 130
5.1 GALERKIN METHOD 130
5.2 RITZ-GALERKIN METHODS 136
5.3 SPECIAL CASES 139
5.4 FREDHOLM-NYSTROEM SYSTEM 144
6 ITERATION METHODS 146
6.1 SIMPLE ITERATIONS 146
6.2 QUADRATURE FORMULAS 150
6.3 ERROR ANALYSIS 153
6.4 ITERATIVE SCHEME 162
6.5 KRYLOV-BOGOLIUBOV METHOD 167
7 SINGULAR EQUATIONS 175
7.1 SINGULARITIES IN LINEAR EQUATIONS 175
7.2 FREDHOLM THEOREMS 178
7.3 MODIFIED QUADRATURE RULE 179
7.4 CONVOLUTION-TYPE KERNELS 181
7.5 VOLTERRA-TYPE SINGULAR EQUATIONS 186
IMAGE 4
CONTENTS VII
7.6 CONVOLUTION METHODS 188
7.6.1 CONVOLUTION OF AN SVK1 188
7.6.2 CONVOLUTION OF AN SVK2 190
7.6.3 ABEL S EQUATION 190
7.6.4 SONINE S EQUATION 192
7.6.5 LOGARITHMIC KERNEL 193
7.7 ASYMPTOTIC METHODS FOR LOG-SINGULAR EQUATIONS 194
7.8 ITERATION METHODS 197
7.8.1 ATKINSON S SCHEME 198
7.8.2 BRAKHAGE S SCHEME 199
7.8.3 ATKINSON S DIRECT SCHEME 201
7.8.4 KELLEY S ALGORITHM 204
7.9 SINGULAR EQUATIONS WITH THE HUBERT KERNEL 207
7.9.1 FIRST-KIND EQUATIONS 207
7.9.2 SECOND-KIND EQUATIONS 209
7.10 FINITE-PART SINGULAR EQUATIONS 210
8 WEAKLY SINGULAR EQUATIONS 213
8.1 WEAKLY SINGULAR KERNEL 213
8.2 TAYLOR S SERIES METHOD 215
8.3 Z/P-APPROXIMATION METHOD 216
8.4 PRODUCT-INTEGRATION METHOD 218
8.4.1 ATKINSON S METHOD 220
8.4.2 GENERALIZATION 226
8.4.3 ATKINSON S MODIFIKATION 228
8.4.4 ASYMPTOTIC EXPANSIONS 231
8.5 SPLINES METHOD 233
8.5.1 FROM SINGULAR SK2 TO IDE 234
8.5.2 5-SPLINE METHOD 235
8.5.3 FROM LOG-SINGULAR TO CAUCHY-SINGULAR 241
8.5.4 ACLASSOF SINGULAR INTEGRALS 242
8.6 WEAKLY SINGULAR VOLTERRA EQUATIONS 244
9 CAUCHY SINGULAR EQUATIONS 252
9.1 CAUCHY SINGULAR EQUATIONS OF THE FIRST KIND 252
9.2 APPROXIMATION BY TRIGONOMETRIE POLYNOMIALS 254
9.3 CAUCHY SINGULAR EQUATIONS OF THE SECOND KIND 258
9.4 FROM CSK2 TO FK2 262
9.5 GAUSS-JACOBI QUADRATURE 264
9.5.1 SOLUTION BY JACOBI POLYNOMIALS 265
9.5.2 COLLOCATION METHOD FOR CSK2 267
9.5.3 A SPECIAL CASE 271
9.5.4 GENERALIZED CAUCHY KERNEL 273
9.6 COLLOCATION METHOD FOR CSK1 276
9.6.1 CANONICAL EQUATION 280
IMAGE 5
VIII CONTENTS
10 SINC-GALERKIN M E T H O DS 286
10.1 SINE FUNCTION APPROXIMATIONS 286
10.2 CONFORMAL MAPS AND INTERPOLATION 289
10.3 APPROXIMATION THEORY 296
10.4 CONVERGENCE 297
10.5 SINC-GALERKIN SCHEME 300
10.6 COMPUTATION GUIDELINES 303
10.7 SINC-COLLOCATION METHOD 304
10.8 SINGLE-LAYER POTENTIAL 310
10.9 DOUBLE-LAYER PROBLEM . 3 20
11 E Q U A T I O NS OF T HE FIRST KIND 321
11.1 INHERENT ILL-POSEDNESS 321
11.2 SEPARABLE KERNELS 323
11.3 SOME THEOREMS 325
11.4 NUMERICAL METHODS 327
11.4.1 QUADRATURE METHOD 327
11.4.2 METHOD OF MOMENTS 332
11.4.3 REGULARIZATION METHODS 333
11.4.4 OTHER REGULARIZATIONS 337
11.4.5 COMPARISON 342
11.4.6 FROMFKL TOFK2 344
11.4.7 EQUATIONS OVER A CONTOUR 346
11.5 VOLTERRA EQUATIONS OF THE FIRST KIND 347
11.5.1 QUADRATURE METHOD 348
11.5.2 METHOD OF LINZ 349
11.5.3 PRODUCT-INTEGRATION METHOD 354
11.6 ABEL S EQUATION 357
11.7 ITERATIVE SCHEMES 361
11.7.1 HANNA AND BROWN S SCHEME 361
11.7.2 VAN DEN BERG S SCHEME 367
12 INVERSION OF LAPLACE TRANSFORMS 375
12.1 LAPLACE TRANSFORMS 375
12.2 GENERAL INTERPOLATING SCHEME 377
12.2.1 INVERSE IN TERMS OF LEGENDRE POLYNOMIALS 378
12.2.2 INVERSE IN TERMS OF SHIFTED LEGENDRE POLYNOMIALS 380
12.2.3 METHOD OFBELLMAN, KALABA, ANDLOCKETT 381
12.2.4 SOLUTION OF THE SYSTEM 382
12.2.5 INVERSE IN TERMS OF LAGUERRE POLYNOMIALS 385
12.2.6 INVERSE IN TERMS OF CHEBYSHEV POLYNOMIALS 393
12.2.7 INVERSE IN TERMS OF JACOBI POLYNOMIALS 396
12.3 INVERSION BY FOURIER SERIES 399
12.3.1 DUBNER AND ABATE S METHOD 399
IMAGE 6
CONTENTS IX
12.3.2 ERROR ANALYSIS 401
12.3.3 EXAMPLES 402
12.3.4 DURBIN S IMPROVEMENT 403
12.3.5 ERROR ANALYSIS 404
12.3.6 EXAMPLES 405
12.4 INVERSION BY THE RIEMANN SUM 410
12.5 APPROXIMATE FORMULAS 412
A Q U A D R A T U RE RULES 416
A. 1 NEWTON-COTES QUADRATURES 416
A.2 GAUSSIAN QUADRATURES 420
A.3 INTEGRATION OF PRODUCTS 423
A.4 SINGULAR INTEGRALS 430
A.5 INFINITE-RANGE INTEGRALS 432
A.6 LINEAR TRANSFORMATION OF QUADRATURES 433
A.7 TRIGONOMETRIE POLYNOMIALS 434
A.8 CONDITION NUMBER 435
A.7 QUADRATURE TABLES 438
B O R T H O G O N AL POLYNOMIALS 444
B.L ZEROS OF SOME ORTHOGONAL POLYNOMIALS 446
C W H I T T A K E R S CARDINAL FUNCTION 452
C.L BASIC RESULTS 452
C.2 APPROXIMATION OF AN INTEGRAL 457
D SINGULAR INTEGRALS 459
D.L CAUCHY S PRINCIPAL-VALUE INTEGRALS 459
D.2 P.V. OF A SINGULAR INTEGRAL ON A CONTOUR 461
D.3 HADAMARD S FINITE-PART INTEGRALS 464
D.4 TWO-SIDED FINITE-PART INTEGRALS 465
D.5 ONE-SIDED FINITE-PART INTEGRALS 467
D.6 EXAMPLES OF CAUCHY P.V. INTEGRALS 468
D.7 EXAMPLES OF HADAMARD S FINITE-PART INTEGRALS 471
BIBLIOGRAPHY 473
SUBJECT I N D EX 501
|
| any_adam_object | 1 |
| author | Kythe, Prem K. 1930- Pratap, Puri |
| author_GND | (DE-588)12072362X |
| author_facet | Kythe, Prem K. 1930- Pratap, Puri |
| author_role | aut aut |
| author_sort | Kythe, Prem K. 1930- |
| author_variant | p k k pk pkk p p pp |
| building | Verbundindex |
| bvnumber | BV014556884 |
| callnumber-first | Q - Science |
| callnumber-label | QA431 |
| callnumber-raw | QA431 |
| callnumber-search | QA431 |
| callnumber-sort | QA 3431 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 640 SK 920 |
| ctrlnum | (OCoLC)48536698 (DE-599)BVBBV014556884 |
| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01838nam a2200469 c 4500</leader><controlfield tag="001">BV014556884</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020709s2002 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">964695685</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764341920</subfield><subfield code="c">(Basel ...) Pp. : EUR 129.00</subfield><subfield code="9">3-7643-4192-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817641920</subfield><subfield code="c">(Boston) Pp.</subfield><subfield code="9">0-8176-4192-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)48536698</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014556884</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA431</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.45</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 640</subfield><subfield code="0">(DE-625)143250:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 920</subfield><subfield code="0">(DE-625)143272:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65R20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kythe, Prem K.</subfield><subfield code="d">1930-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)12072362X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computational methods for linear integral equations</subfield><subfield code="c">Prem K. Kythe ; Pratap Puri</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston ; Basel ; Berlin</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 508 S.</subfield><subfield code="b">graph. Darst. : 24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 473 - 508</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Integraalvergelijkingen</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral equations</subfield><subfield code="x">Numerical solutions</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare Integralgleichung</subfield><subfield code="0">(DE-588)4114426-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare Integralgleichung</subfield><subfield code="0">(DE-588)4114426-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pratap, Puri</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009898655</subfield></datafield></record></collection> |
| id | DE-604.BV014556884 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:31Z |
| institution | BVB |
| isbn | 3764341920 0817641920 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009898655 |
| oclc_num | 48536698 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-83 |
| owner_facet | DE-703 DE-634 DE-83 |
| physical | XVIII, 508 S. graph. Darst. : 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Kythe, Prem K. 1930- Verfasser (DE-588)12072362X aut Computational methods for linear integral equations Prem K. Kythe ; Pratap Puri Boston ; Basel ; Berlin Birkhäuser 2002 XVIII, 508 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 473 - 508 Integraalvergelijkingen gtt Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Pratap, Puri Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kythe, Prem K. 1930- Pratap, Puri Computational methods for linear integral equations Integraalvergelijkingen gtt Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4114426-0 |
| title | Computational methods for linear integral equations |
| title_auth | Computational methods for linear integral equations |
| title_exact_search | Computational methods for linear integral equations |
| title_full | Computational methods for linear integral equations Prem K. Kythe ; Pratap Puri |
| title_fullStr | Computational methods for linear integral equations Prem K. Kythe ; Pratap Puri |
| title_full_unstemmed | Computational methods for linear integral equations Prem K. Kythe ; Pratap Puri |
| title_short | Computational methods for linear integral equations |
| title_sort | computational methods for linear integral equations |
| topic | Integraalvergelijkingen gtt Integral equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Integraalvergelijkingen Integral equations Numerical solutions Numerisches Verfahren Lineare Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009898655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kythepremk computationalmethodsforlinearintegralequations AT pratappuri computationalmethodsforlinearintegralequations |