PUBLICATIONS 

2. Singular boundary resonance and turning point resonance, (with F.B.Hanson), SIAM J. Appl. Math., 46 (1986), 962-977.

3. Singular and turning point resonance: Small perturbations- big effects, (with F.B.Hanson), Appl. Math.Letters, 1 (1988), 137-140.

4. Two turning points of second order, SIAM J. Appl. Math., 50 (1988), 883-892.

5. A modified third order Runge-Kutta method, Appl. Math.Letters, 3 (1990), 123-125.

6. Moments of extinction for a singular perturbation problem in the diffusion process, (with F. B. Hanson), SIAM J. Appl. Math., 51 (1991), 233-265.

7. On the asymptotic solutions of a differential equation with multiple singular points, Journal of Computational and Applied Mathematics, 34 (1991), 65-74.

8. Modified numerical methods based on arithmetic and geometric means, Appl. Math.Letters, 4 (1991), 49-52.

9. Asymptotic solutions of an eigenvalue problem with several second turning points, IMA J. of Appl. Math., 48 (1992), 39-51.

10. Sequences of series, Appl. Math. Letters, 5 (1992), 39-43.

11. Resonance and asymptotic solutions of a singular perturbation problem, IMA J. of Appl. Math., 49 (1992), 231-244.

12. A Comparison of Modified Runge-Kutta Methods Based on a Variety of Means, Intern. J. Computer Math., 50 (1994), 105-112.

13. On the Numerical solution of the Goursat Problem, Applied Mathematics and Computation, 59 (1993), 89-95.

14. On the Numerical solution of y' = f(x,y) by a class of nonlinear trapezoidal formulas, Intern. J. Computer Math., 51 (1994), 229-238.

15. The Decomposition Method for Approximate solution to the Goursat Problem, Applied Mathematics and Computation, 69 (1995), 299-311.

16. A new approach to the nonlinear advection problem: An application of the decomposition method, Applied Mathematics and Computation, 72 (1995), 175-181.

17. Two methods for solving integral equations, (with S. Khuri), Applied Mathematics and Computation, 77 (1996), 79-89.

18. On the solution of the fourth order parabolic equation by the decomposition method, Intern. J. Computer Math.,(1995),57, 213-217.

19. The solution of a partial differential equation arising in fluid flow theory, (with S. Khuri), Applied Mathematics and Computation, 77 (1996), 295-300.

20. A reliable technique for solving the weakly-singular second-kind Volterra-type integral equations, (with S. Khuri), Applied Mathematics and Computation, 80 (1996), 287-299.

21. The decomposition method for solving a second Fredholm second kind integral equation with a logarithmic kernel, (with S. Khuri), Intern. J.Computer Math. 61, (1996), 103-110 .

22. Necessary conditions for the appearance of noise terms in decomposition solution series, Applied Mathematics and Computation, 81, (1997), 265 - 274.

23. On the solution of a partial differential equation arising in Stokes flow, (with S. Khuri), Applied Mathematics and Computation, 85 (1997), 139 - 147.

24. A study on a boundary-layer equation arising in an incompressible fluid, Applied Mathematics and Computation, 87 (1997), 199 - 204.

25. A study on complex integrals involving absolute values, Applied Mathematics and Computation, 85,(1997), 281 - 286 .

26. Equality of partial solutions in the decomposition method for partial differential equations, Intern. J. Computer Math., 65 (1997), 293 - 308.

27. New ideas for solving size-structured population models, (with S. Khuri), Applied Mathematics and Computation, 93, (1998), 91-96.

28. A reliable technique for solving the wave equation in an infinite one-dimensional medium, Applied Mathematics and Computation, 92 (1998), 1 - 7.

29. A comparison between the Adomian decomposition method and the Taylor series method in the series solutions, Applied Mathematics and Computation, 97(1998), 37 - 44.

30. A comparative study on a singular perturbation problem with two singular boundary points, Applied Mathematics and Computation, 99 (1999), 179-193.

31. Analytical approximations and Pade' approximants for Volterra's population model, Applied Mathematics and Computation, 100 (1999), 13-25.

32. A reliable modification of the Adomian decomposition method, Applied Mathematics and Computation, 102 (1999), 77-86.

33. The modified decomposition method and the Pade' approximants for solving Thomas-Fermi equation, Mathematics and Computation, 105 (1999), 11 - 19.

34. A new technique for calculating Adomian polynomials for nonlinear polynomials, Applied Mathematics and Computation, 111(1)(2000),33-51.

35. The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model, Applied Mathematics and Computation 110 (2000), 251-264.

36. The modified decomposition method applied to unsteady  flow of gas through a porous medium, Applied Mathematics and Computation, 118(2/3) (2001) 123-132.

37. A new algorithm for solving differential equations of the Lane-Emden type, (1999), Applied Mathematics and Computation, 118(2/3) (2001) 287-310.

38. The numerical solution of special fourth-order boundary value problems by the modified decomposition method, International J. of Computer Mathematics, 79(3) (2002)  345-356.

39. The numerical solution of fifth-order boundary value problems by the decomposition method, (1999), Journal of Computational and Applied Mathematics, 136(1/2) (2001), 259-270.

40. The numerical solution of sixth-order boundary value problems by the modified decomposition method, Applied Mathematics and Computation, 118 (2/3) (2001) 311-325.

41. The numerical solution of eighth-order boundary value problems by the modified decomposition method, Neural, Parallel and Scientific Computations, 8(2) (2000) 133-146.

42. Approximate solutions to boundary value problems of higher-order by the modified decomposition method, Computers and Mathematics with Applications, 40 (2000) 679- 691.

43. A reliable algorithm for solving boundary value problems for higher-order integro-differential equations, (1999), Applied Mathematics and Computation, 118 (2/3) (2001) 327-342.

44. The decomposition method for higher dimensional initial boundary value problems of variable coefficients,  International Journal of Computer Mathematics, 76 (2000), 159-172.

45. The modified decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth order, International J. of Nonlinear Sciences and Numerical Simulation, 1 (2000) 17-24.

46. A new method for solving singular initial value problems in the second order ordinary differential equations, Applied mathematics and Computation, 28(1) (2002), 45-47.

47. Exact solutions to nonlinear diffusion equations by the decomposition method, Applied Mathematics and Computation, 123 (1) (2001) 109-122 .

48. A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation, Applied Mathematics and Computation, 123(2) (2001) 205-217.

49. Analytic treatment for variable coefficient fourth-order parabolic partial differential equations, Applied Mathematics and Computation, 123 (2) (2001) 219-227.

50. Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, Solitons and Fractals,  12(8) (2001) 1549-1556.

51. An analytic study on  the third-order dispersive partial differential equations, Applied Mathematics and Computation, 142 (2-3) (2002)  511-520.

52. The decomposition method for solving the diffusion equation subject to the classification of mass, International J. of Applied Mathematics (IJAM), 3(1) (2000) 53-69. 

53. A note on using Adomian decomposition method for solving boundary value problems, Foundations of Physics Letters,13(5) (2000) 493-498.

54. A new modification of Adomian decomposition method for linear and nonlinear operators, (with S. El-Sayed), Applied Mathematics and Computation, 123(3) (2001) 393-405.

55. Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions, Applied Mathematics and Computation,123 (2001) 133-140.

56. Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method, Chaos, Solitons and Fractals,  12(12) (2001) 2283-2293.

57. Solitary wave solutions for the modified KdV equation by Adomian decomposition method, International J. of Applied Mathematics (IJAM), 3(4)  (2000) 361-368.

58. A reliable treatment for mixed Volterra-Fredholm integral equations, Applied Mathematics and Computation,  127 (2002), 405-414.

59. A reliable technique for solving linear and nonlinear Schrodinger equations by Adomian decomposition method, Bulletin of the Institute of Mathematics,(29(2)  (2001),  125-134.

60. Existence and construction of compacton solutions, Chaos, Solitons and Fractals, 19(3) (2004) 463-470. 

61. A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Comput. Math. Applic., 41 (2001) 1237-1244.

62. New solitary-wave solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos, Solitons and Fractals, 13(20 (2002) 321-330.

63. Exact special solutions with solitary patterns for the nonlinear dispersive K(m,n) equations, Chaos, Solitons and Fractals, 13(1) (2001), 161-170.

64. A reliable algorithm for higher-dimensional diffusion equation subject to the classification of mass, International J. of Applied Mathematics, 7(3)  (2001) to 65-74.

65. Exact solutions for variable coefficient fourth-order parabolic partial differential equations in higher dimensional spaces, Applied mathematics and Computation, 130 (2/3)  (2002) 415-424 .

66. Compactons dispersive structures for variants of the K(n,n) and the KP equations, Chaos, Solitons and Fractals,  13(5) (2002) 1053-1062.

67. Compactons and solitary patterns structures for variants of the KdV and the KP equations, Applied mathematics and Computation, 139(1) (2003) 37-54.

68. Compactons structures for fifth-order KdV like equations in higher dimensions, Applied Mathematics and Computation,  130 (2/3) (2002) 425-440 .

69. Solitary patterns solutions having infinite slopes or cusps for fifth-order KdV like equations in higher dimensions, Applied mathematics and Computation, 131/1 (2002) 181-194.

70. A study of nonlinear dispersive equations with solitary-wave solutions having compact support, Mathematics and Computers in Simulation, 56 (2001) 269-276.

71. Compact and noncompact structures for variants of the KdV equation, Applied Mathematics and Computation,    132 (1)(2002) 29-45.

72. General compactons solutions for the focusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Applied Mathematics and Computation, 133(2/3) (2002), 213-227.

73. General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Applied Mathematics and Computation, 133(2/3) (2002), 229-244.

74. Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation, Applied Mathematics and Computation, 134(2/3)  (2003) , 487-500.

75. General compactons solutions  and solitary patterns solutions for modified   nonlinear dispersive equations m K(n,n)  in higher dimensional spaces, Mathematics and Computers in Simulation, 59 (2002), 519-531.

76. The effect of the order of the nonlinear dispersive equation on the compact and the noncompact solutions, Appl. Math. Comput.,  138 (2/3) (2003 )  309-319.

77. Several new exact solutions for a fast diffusion equation by the differential constraints of the linear determining equations,  Applied Mathematics and Computation, 145(2/3) (2003) 525-540.

78. Compact and noncompact structures formed by nonlinear equations with positive and negative exponents, Applied Mathematics and Computation, 146(1) (2003) 1-25.

79. Compacton solutions and nonlinear dispersion,  Applied Mathematics and Computation, 142(2-3) (2003)  495-509.

80. Compacton solutions of the Kawahara-type nonlinear dispersive equation, Applied Mathematics and Computation, 145 (1) (2003)  133-150.

81. The existence of noise terms for systems of inhomogeneous differential and integral equations, Applied Mathematics and Computation, 146 (1) (2003) 81-92.

83. A study on compacton-like solutions for the modified KdV and fifth order KdV-like equations,  Applied Mathematics and Computation, 147(2) (2004), 439-447.

84. Compacton solutions of higher order nonlinear dispersive KdV-like equations, Applied Mathematics and Computation, 147(2) (2004), 449-460.

85. Compact and noncompact structures in a class of nonlinearly dispersive equations, ( with Thiab Taha), Computers and Mathematics in Simulation, 62(1-2)  (2003), 171-189.

86. An analytic study of compactons solutions for variants of Kuramoto-Sivanshinsky equation, Applied Mathematics and Computation, 148 (2004),  571- 585. 

87. Compact structures for variants of the generalized KdV and the generalized KP equations,   Applied Mathematics and Computation, 149(1) (2004) 103-117.

88. A study on nonlinear dispersive partial differential equations of compact and non compact solutions,  Applied Mathematics and Computation, 135 (2-3) (2003) 399-409.

89. A construction of compact and noncompact solutions for nonlinear dispersive equations of even order,  Applied Mathematics and Computation, 135 (2-3) (2003) 411-424.

90. Compactons in a class of nonlinear dispersive equations, Mathematical and Computer Modelling, 37(3/4) (2003) 333-341.

91. An analytic study of compactons structures in a class of nonlinear dispersive equations,  Mathematics and Computers in Simulation, 63(1) (2003) 35-44 .

92. Exact solutions of heat-like and wave-like equations with variable coefficients (with Alice Gorguis), Applied Mathematics and Computation, 149(1) (2004) 15-29.

93. Compactons structures for specific nonlinear dispersive equations, Applied Mathematics and Computation, 150 (2) (2004) 399-407.

94. Distinct variants of the KdV equation with compact and noncompact structures, Applied Mathematics and Computation, 150 (2) (2004) 365-377.

95. Variants of the generalized KdV equation with compact and noncompact structures,  Computers and Mathematics with Applications, 47 (2004) 583-591.

96. An analytic study of Fisher's equation by using Adomian decomposition method, (with Alice Gorguis), Applied Mathematics and Computation, 154(3)  609--620 (2004).

97. Two classes of variants of the generalized KdV equations with compact and noncompact solutions, Applied Mathematics and Computation, 154(3) 835--846 (2004).

98. The tanh method for travelling wave solutions of nonlinear equations, Applied Mathematics and Computation, 154 (3) 713--723 (2004).

99. Compact and noncompact solutions for nonlinear dispersive variants of the generalized KdV equation, Applied Mathematics and Computation,  159(2) (2004)  577-588.

100. The sine-cosine method for obtaining solutions with compact and noncompact structures, Applied Mathematics and Computation,  159(2) (2004) 559-576.

101. Effect of the nonlinearity of the middle term for variants of the generalized KdV equation, Applied Mathematics and Computation,  159(2) (2004) 539-558.

102. Adomian decomposition method for a reliable treatment of the Emden-Fowler equation, Applied Mathematics and Computation,  161(2005),543-560.

103. Variants of the generalized fifth-order KdV equation with compact and noncompact structures, (with M.A.Helal), Chaos, Solitons and Fractals, 21 (2004) 579-589(2004).

104. Compactons, solitons and periodic solutions for variants of the KdV and the KP equations, Applied  Mathematics and Computation, 161(2005) 561-575.

105. Nonlinear dispersive special type of the Zakharov-Kuznetsov equation ZK(n,n) with Compact and noncompact structures, Applied mathematics and Computation, 161 (2005) 577-590.

106. A sine-cosine method for handling nonlinear wave equations, Mathematical and Computer Modelling, 40 (2004) 499-508.

107. New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations,  Chaos, Solitons and Compactons, 22(1) 249-260 (2004).

108. Nonlinear variants  of KdV and KP equations with compactons, solitons and periodic solutions, Communications in Nonlinear Science and Numerical Simulation, 10(4) (2005) 451-463.

109. Special types of the nonlinear dispersive Zakharov-Kuznetsov equation with compactons, solitons and periodic solutions, International Journal of Computer Mathematics, 81 (9) 1107-1119 (2004).

110. Exact solutions with solitons and periodic structures for the Zakharov-Kuznetsov (ZK) equation  and its modified form, Communications in Nonlinear Science and Numerical Simulation, 10 (2005) 597- 606.

111. A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompact solutions,  Applied  Mathematics and Computation,  165 (2005) 485-501.

112.  A reliable treatment of the physical structure for the nonlinear equation K(m,n), Applied  Mathematics and Computation, 163(3) (2005) 1081-1095.

113.  New compact and noncompact solutions for two variants of a modified Camassa-Holm equation, Applied  Mathematics and Computation, 163 (3) (2005) 1165-1179.

114. Exact solutions with compact and noncompact structures for the one-dimensional generalized Benjamin-Bona-mahony equation,  Communications in Nonlinear Science and Numerical Simulation, 10 (2005) 855-867.

115. Adomian decomposition method for a reliable treatment of the Bratu-type equations, Applied  Mathematics and Computation, 166(3) (2005), 652-663.

116. Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method,  Applied  Mathematics and Computation, 166(3) (2005) 638-651.

117. Generalized Boussinesq type of equations with compactons, solitons and periodic solutions,  Applied  Mathematics and Computation, 167(2) (2005), 1162-1178.

118. Variants of the Two-Dimensional Boussinesq Equations with Compactons, Solitons and periodic Solutions, Computers and Mathematics with Applications, 49 (2005) 295-301.

119. The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants,  Communications in Nonlinear Science and Numerical Simulation, 11(2) (2006) 148-160.

120. Generalized forms of the Phi-Four equation with compactons, solitons and periodic solutions, Mathematics and Computers in Simulation, Special Issue on Nonlinear waves: Computation and Theory IV, 69 (5-6) (2005)  580-588.

121. The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation, Applied  Mathematics and Computation, 167(2) (2005), 1179-1195.